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Simplifying x2 + -32x + 64 = 49 Reorder the terms: 64 + -32x + x2 = 49 Solving 64 + -32x + x2 = 49 Solving for variable 'x'. Reorder the terms: 64 + -49 + -32x + x2 = 49 + -49 Combine like terms: 64 + -49 = 15 15 + -32x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 15 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -32x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -32x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -32x + x2 = 0 + -15 -32x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -32x + x2 = -15 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -15 + 256 Reorder the terms: 256 + -32x + x2 = -15 + 256 Combine like terms: -15 + 256 = 241 256 + -32x + x2 = 241 Factor a perfect square on the left side: (x + -16)(x + -16) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + -16) equal to 15.524174696 and -15.524174696.Subproblem 1
x + -16 = 15.524174696 Simplifying x + -16 = 15.524174696 Reorder the terms: -16 + x = 15.524174696 Solving -16 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 15.524174696 + 16 Combine like terms: -16 + 16 = 0 0 + x = 15.524174696 + 16 x = 15.524174696 + 16 Combine like terms: 15.524174696 + 16 = 31.524174696 x = 31.524174696 Simplifying x = 31.524174696Subproblem 2
x + -16 = -15.524174696 Simplifying x + -16 = -15.524174696 Reorder the terms: -16 + x = -15.524174696 Solving -16 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -15.524174696 + 16 Combine like terms: -16 + 16 = 0 0 + x = -15.524174696 + 16 x = -15.524174696 + 16 Combine like terms: -15.524174696 + 16 = 0.475825304 x = 0.475825304 Simplifying x = 0.475825304Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.524174696, 0.475825304}
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