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Simplifying 7x(x + 8) = 84 Reorder the terms: 7x(8 + x) = 84 (8 * 7x + x * 7x) = 84 (56x + 7x2) = 84 Solving 56x + 7x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 56x + 7x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 56x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-12 + 8x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-12 + 8x + x2)' equal to zero and attempt to solve: Simplifying -12 + 8x + x2 = 0 Solving -12 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 8x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 8x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8x + x2 = 0 + 12 8x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 8x + x2 = 12 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 12 + 16 Reorder the terms: 16 + 8x + x2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8x + x2 = 28 Factor a perfect square on the left side: (x + 4)(x + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 4 = 5.291502622 Simplifying x + 4 = 5.291502622 Reorder the terms: 4 + x = 5.291502622 Solving 4 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.291502622 + -4 x = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 x = 1.291502622 Simplifying x = 1.291502622Subproblem 2
x + 4 = -5.291502622 Simplifying x + 4 = -5.291502622 Reorder the terms: 4 + x = -5.291502622 Solving 4 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.291502622 + -4 x = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 x = -9.291502622 Simplifying x = -9.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.291502622, -9.291502622}Solution
x = {1.291502622, -9.291502622}
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