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Simplifying 7x(x + 8) + -7 + 15 = 100 Reorder the terms: 7x(8 + x) + -7 + 15 = 100 (8 * 7x + x * 7x) + -7 + 15 = 100 (56x + 7x2) + -7 + 15 = 100 Reorder the terms: -7 + 15 + 56x + 7x2 = 100 Combine like terms: -7 + 15 = 8 8 + 56x + 7x2 = 100 Solving 8 + 56x + 7x2 = 100 Solving for variable 'x'. Reorder the terms: 8 + -100 + 56x + 7x2 = 100 + -100 Combine like terms: 8 + -100 = -92 -92 + 56x + 7x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -92 + 56x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -13.14285714 + 8x + x2 = 0 Move the constant term to the right: Add '13.14285714' to each side of the equation. -13.14285714 + 8x + 13.14285714 + x2 = 0 + 13.14285714 Reorder the terms: -13.14285714 + 13.14285714 + 8x + x2 = 0 + 13.14285714 Combine like terms: -13.14285714 + 13.14285714 = 0.00000000 0.00000000 + 8x + x2 = 0 + 13.14285714 8x + x2 = 0 + 13.14285714 Combine like terms: 0 + 13.14285714 = 13.14285714 8x + x2 = 13.14285714 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 = 13.14285714 + 16 Reorder the terms: 16 + 8x + x2 = 13.14285714 + 16 Combine like terms: 13.14285714 + 16 = 29.14285714 16 + 8x + x2 = 29.14285714 Factor a perfect square on the left side: (x + 4)(x + 4) = 29.14285714 Calculate the square root of the right side: 5.398412465 Break this problem into two subproblems by setting (x + 4) equal to 5.398412465 and -5.398412465.Subproblem 1
x + 4 = 5.398412465 Simplifying x + 4 = 5.398412465 Reorder the terms: 4 + x = 5.398412465 Solving 4 + x = 5.398412465 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 = 5.398412465 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.398412465 + -4 x = 5.398412465 + -4 Combine like terms: 5.398412465 + -4 = 1.398412465 x = 1.398412465 Simplifying x = 1.398412465Subproblem 2
x + 4 = -5.398412465 Simplifying x + 4 = -5.398412465 Reorder the terms: 4 + x = -5.398412465 Solving 4 + x = -5.398412465 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 = -5.398412465 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.398412465 + -4 x = -5.398412465 + -4 Combine like terms: -5.398412465 + -4 = -9.398412465 x = -9.398412465 Simplifying x = -9.398412465Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.398412465, -9.398412465}
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