Final answer:
To complete the calculation x(x + 4)+8x(2x+1)=7x( x + 4), you need to find the values of x that satisfy the equation. By simplifying and solving the equation step by step, the numbers that should go in the boxes are x = 0 and x = 8/5 or 1.6.
Step-by-step explanation:
To complete the calculation x(x + 4)+8x(2x+1)=7x( x + 4), we need to find the values of x that satisfy the equation. Let's simplify the equation step by step:
- Distribute x to both terms inside the first parentheses and simplify: x^2 + 4x
- Distribute 8x to both terms inside the second parentheses and simplify: 16x^2 + 8x
- Distribute 7x to both terms inside the third parentheses and simplify: 7x^2 + 28x
- Now, rewrite the equation with the simplified terms: x^2 + 4x + 16x^2 + 8x = 7x^2 + 28x
- Combine like terms on both sides of the equation: 17x^2 + 12x = 7x^2 + 28x
- Move all terms to one side to form a quadratic equation: 17x^2 + 12x - 7x^2 - 28x = 0
- Combine like terms again: 10x^2 - 16x = 0
- Factor out common terms: 2x(5x - 8) = 0
- Set each factor equal to zero and solve for x: 2x = 0 or 5x - 8 = 0
- For 2x = 0, divide both sides by 2 to get x = 0
- For 5x - 8 = 0, add 8 to both sides and divide by 5 to get x = 8/5 or 1.6
Therefore, the numbers that should go in the boxes to complete the calculation are x = 0 and x = 8/5 or 1.6.