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Simplifying x2 + -16x + -36 = 100 Reorder the terms: -36 + -16x + x2 = 100 Solving -36 + -16x + x2 = 100 Solving for variable 'x'. Reorder the terms: -36 + -100 + -16x + x2 = 100 + -100 Combine like terms: -36 + -100 = -136 -136 + -16x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -136 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + -16x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + -16x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + -16x + x2 = 0 + 136 -16x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 -16x + x2 = 136 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 = 136 + 64 Reorder the terms: 64 + -16x + x2 = 136 + 64 Combine like terms: 136 + 64 = 200 64 + -16x + x2 = 200 Factor a perfect square on the left side: (x + -8)(x + -8) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -8) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -8 = 14.142135624 Simplifying x + -8 = 14.142135624 Reorder the terms: -8 + x = 14.142135624 Solving -8 + x = 14.142135624 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 = 14.142135624 + 8 Combine like terms: -8 + 8 = 0 0 + x = 14.142135624 + 8 x = 14.142135624 + 8 Combine like terms: 14.142135624 + 8 = 22.142135624 x = 22.142135624 Simplifying x = 22.142135624Subproblem 2
x + -8 = -14.142135624 Simplifying x + -8 = -14.142135624 Reorder the terms: -8 + x = -14.142135624 Solving -8 + x = -14.142135624 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 = -14.142135624 + 8 Combine like terms: -8 + 8 = 0 0 + x = -14.142135624 + 8 x = -14.142135624 + 8 Combine like terms: -14.142135624 + 8 = -6.142135624 x = -6.142135624 Simplifying x = -6.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.142135624, -6.142135624}
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