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Simplifying 2x + 13 + -1x2 + 14x + 49 = 0 Reorder the terms: 13 + 49 + 2x + 14x + -1x2 = 0 Combine like terms: 13 + 49 = 62 62 + 2x + 14x + -1x2 = 0 Combine like terms: 2x + 14x = 16x 62 + 16x + -1x2 = 0 Solving 62 + 16x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -62 + -16x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -16x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -16x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -16x + x2 = 0 + 62 -16x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -16x + x2 = 62 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 62 + 64 Reorder the terms: 64 + -16x + x2 = 62 + 64 Combine like terms: 62 + 64 = 126 64 + -16x + x2 = 126 Factor a perfect square on the left side: (x + -8)(x + -8) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + -8) equal to 11.22497216 and -11.22497216.Subproblem 1
x + -8 = 11.22497216 Simplifying x + -8 = 11.22497216 Reorder the terms: -8 + x = 11.22497216 Solving -8 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 11.22497216 + 8 Combine like terms: -8 + 8 = 0 0 + x = 11.22497216 + 8 x = 11.22497216 + 8 Combine like terms: 11.22497216 + 8 = 19.22497216 x = 19.22497216 Simplifying x = 19.22497216Subproblem 2
x + -8 = -11.22497216 Simplifying x + -8 = -11.22497216 Reorder the terms: -8 + x = -11.22497216 Solving -8 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -11.22497216 + 8 Combine like terms: -8 + 8 = 0 0 + x = -11.22497216 + 8 x = -11.22497216 + 8 Combine like terms: -11.22497216 + 8 = -3.22497216 x = -3.22497216 Simplifying x = -3.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.22497216, -3.22497216}
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