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Simplifying x2 + -7 = 16x Reorder the terms: -7 + x2 = 16x Solving -7 + x2 = 16x Solving for variable 'x'. Reorder the terms: -7 + -16x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -7 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -16x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -16x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -16x + x2 = 0 + 7 -16x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -16x + x2 = 7 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 = 7 + 64 Reorder the terms: 64 + -16x + x2 = 7 + 64 Combine like terms: 7 + 64 = 71 64 + -16x + x2 = 71 Factor a perfect square on the left side: (x + -8)(x + -8) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -8) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -8 = 8.426149773 Simplifying x + -8 = 8.426149773 Reorder the terms: -8 + x = 8.426149773 Solving -8 + x = 8.426149773 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 = 8.426149773 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.426149773 + 8 x = 8.426149773 + 8 Combine like terms: 8.426149773 + 8 = 16.426149773 x = 16.426149773 Simplifying x = 16.426149773Subproblem 2
x + -8 = -8.426149773 Simplifying x + -8 = -8.426149773 Reorder the terms: -8 + x = -8.426149773 Solving -8 + x = -8.426149773 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 = -8.426149773 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.426149773 + 8 x = -8.426149773 + 8 Combine like terms: -8.426149773 + 8 = -0.426149773 x = -0.426149773 Simplifying x = -0.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.426149773, -0.426149773}
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