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Simplifying 916 = 7x2 + 84x + 15 Reorder the terms: 916 = 15 + 84x + 7x2 Solving 916 = 15 + 84x + 7x2 Solving for variable 'x'. Combine like terms: 916 + -15 = 901 901 + -84x + -7x2 = 15 + 84x + 7x2 + -15 + -84x + -7x2 Reorder the terms: 901 + -84x + -7x2 = 15 + -15 + 84x + -84x + 7x2 + -7x2 Combine like terms: 15 + -15 = 0 901 + -84x + -7x2 = 0 + 84x + -84x + 7x2 + -7x2 901 + -84x + -7x2 = 84x + -84x + 7x2 + -7x2 Combine like terms: 84x + -84x = 0 901 + -84x + -7x2 = 0 + 7x2 + -7x2 901 + -84x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 901 + -84x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -128.7142857 + 12x + x2 = 0 Move the constant term to the right: Add '128.7142857' to each side of the equation. -128.7142857 + 12x + 128.7142857 + x2 = 0 + 128.7142857 Reorder the terms: -128.7142857 + 128.7142857 + 12x + x2 = 0 + 128.7142857 Combine like terms: -128.7142857 + 128.7142857 = 0.0000000 0.0000000 + 12x + x2 = 0 + 128.7142857 12x + x2 = 0 + 128.7142857 Combine like terms: 0 + 128.7142857 = 128.7142857 12x + x2 = 128.7142857 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 128.7142857 + 36 Reorder the terms: 36 + 12x + x2 = 128.7142857 + 36 Combine like terms: 128.7142857 + 36 = 164.7142857 36 + 12x + x2 = 164.7142857 Factor a perfect square on the left side: (x + 6)(x + 6) = 164.7142857 Calculate the square root of the right side: 12.834106346 Break this problem into two subproblems by setting (x + 6) equal to 12.834106346 and -12.834106346.Subproblem 1
x + 6 = 12.834106346 Simplifying x + 6 = 12.834106346 Reorder the terms: 6 + x = 12.834106346 Solving 6 + x = 12.834106346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 12.834106346 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.834106346 + -6 x = 12.834106346 + -6 Combine like terms: 12.834106346 + -6 = 6.834106346 x = 6.834106346 Simplifying x = 6.834106346Subproblem 2
x + 6 = -12.834106346 Simplifying x + 6 = -12.834106346 Reorder the terms: 6 + x = -12.834106346 Solving 6 + x = -12.834106346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -12.834106346 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.834106346 + -6 x = -12.834106346 + -6 Combine like terms: -12.834106346 + -6 = -18.834106346 x = -18.834106346 Simplifying x = -18.834106346Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.834106346, -18.834106346}
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