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Simplifying x2 + -1x + -15625 = 0 Reorder the terms: -15625 + -1x + x2 = 0 Solving -15625 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15625' to each side of the equation. -15625 + -1x + 15625 + x2 = 0 + 15625 Reorder the terms: -15625 + 15625 + -1x + x2 = 0 + 15625 Combine like terms: -15625 + 15625 = 0 0 + -1x + x2 = 0 + 15625 -1x + x2 = 0 + 15625 Combine like terms: 0 + 15625 = 15625 -1x + x2 = 15625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 15625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 15625 + 0.25 Combine like terms: 15625 + 0.25 = 15625.25 0.25 + -1x + x2 = 15625.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 15625.25 Calculate the square root of the right side: 125.000999996 Break this problem into two subproblems by setting (x + -0.5) equal to 125.000999996 and -125.000999996.Subproblem 1
x + -0.5 = 125.000999996 Simplifying x + -0.5 = 125.000999996 Reorder the terms: -0.5 + x = 125.000999996 Solving -0.5 + x = 125.000999996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 125.000999996 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 125.000999996 + 0.5 x = 125.000999996 + 0.5 Combine like terms: 125.000999996 + 0.5 = 125.500999996 x = 125.500999996 Simplifying x = 125.500999996Subproblem 2
x + -0.5 = -125.000999996 Simplifying x + -0.5 = -125.000999996 Reorder the terms: -0.5 + x = -125.000999996 Solving -0.5 + x = -125.000999996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -125.000999996 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -125.000999996 + 0.5 x = -125.000999996 + 0.5 Combine like terms: -125.000999996 + 0.5 = -124.500999996 x = -124.500999996 Simplifying x = -124.500999996Solution
The solution to the problem is based on the solutions from the subproblems. x = {125.500999996, -124.500999996}
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