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Simplifying x2 + -32x = -28 Reorder the terms: -32x + x2 = -28 Solving -32x + x2 = -28 Solving for variable 'x'. Reorder the terms: 28 + -32x + x2 = -28 + 28 Combine like terms: -28 + 28 = 0 28 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -32x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -32x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -32x + x2 = 0 + -28 -32x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -32x + x2 = -28 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 = -28 + 256 Reorder the terms: 256 + -32x + x2 = -28 + 256 Combine like terms: -28 + 256 = 228 256 + -32x + x2 = 228 Factor a perfect square on the left side: (x + -16)(x + -16) = 228 Calculate the square root of the right side: 15.099668871 Break this problem into two subproblems by setting (x + -16) equal to 15.099668871 and -15.099668871.Subproblem 1
x + -16 = 15.099668871 Simplifying x + -16 = 15.099668871 Reorder the terms: -16 + x = 15.099668871 Solving -16 + x = 15.099668871 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 = 15.099668871 + 16 Combine like terms: -16 + 16 = 0 0 + x = 15.099668871 + 16 x = 15.099668871 + 16 Combine like terms: 15.099668871 + 16 = 31.099668871 x = 31.099668871 Simplifying x = 31.099668871Subproblem 2
x + -16 = -15.099668871 Simplifying x + -16 = -15.099668871 Reorder the terms: -16 + x = -15.099668871 Solving -16 + x = -15.099668871 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 = -15.099668871 + 16 Combine like terms: -16 + 16 = 0 0 + x = -15.099668871 + 16 x = -15.099668871 + 16 Combine like terms: -15.099668871 + 16 = 0.900331129 x = 0.900331129 Simplifying x = 0.900331129Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.099668871, 0.900331129}
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