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Simplifying 128x2 + -90x + 15 = 0 Reorder the terms: 15 + -90x + 128x2 = 0 Solving 15 + -90x + 128x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 128 the coefficient of the squared term: Divide each side by '128'. 0.1171875 + -0.703125x + x2 = 0 Move the constant term to the right: Add '-0.1171875' to each side of the equation. 0.1171875 + -0.703125x + -0.1171875 + x2 = 0 + -0.1171875 Reorder the terms: 0.1171875 + -0.1171875 + -0.703125x + x2 = 0 + -0.1171875 Combine like terms: 0.1171875 + -0.1171875 = 0.0000000 0.0000000 + -0.703125x + x2 = 0 + -0.1171875 -0.703125x + x2 = 0 + -0.1171875 Combine like terms: 0 + -0.1171875 = -0.1171875 -0.703125x + x2 = -0.1171875 The x term is -0.703125x. Take half its coefficient (-0.3515625). Square it (0.1235961914) and add it to both sides. Add '0.1235961914' to each side of the equation. -0.703125x + 0.1235961914 + x2 = -0.1171875 + 0.1235961914 Reorder the terms: 0.1235961914 + -0.703125x + x2 = -0.1171875 + 0.1235961914 Combine like terms: -0.1171875 + 0.1235961914 = 0.0064086914 0.1235961914 + -0.703125x + x2 = 0.0064086914 Factor a perfect square on the left side: (x + -0.3515625)(x + -0.3515625) = 0.0064086914 Calculate the square root of the right side: 0.080054303 Break this problem into two subproblems by setting (x + -0.3515625) equal to 0.080054303 and -0.080054303.Subproblem 1
x + -0.3515625 = 0.080054303 Simplifying x + -0.3515625 = 0.080054303 Reorder the terms: -0.3515625 + x = 0.080054303 Solving -0.3515625 + x = 0.080054303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3515625' to each side of the equation. -0.3515625 + 0.3515625 + x = 0.080054303 + 0.3515625 Combine like terms: -0.3515625 + 0.3515625 = 0.0000000 0.0000000 + x = 0.080054303 + 0.3515625 x = 0.080054303 + 0.3515625 Combine like terms: 0.080054303 + 0.3515625 = 0.431616803 x = 0.431616803 Simplifying x = 0.431616803Subproblem 2
x + -0.3515625 = -0.080054303 Simplifying x + -0.3515625 = -0.080054303 Reorder the terms: -0.3515625 + x = -0.080054303 Solving -0.3515625 + x = -0.080054303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3515625' to each side of the equation. -0.3515625 + 0.3515625 + x = -0.080054303 + 0.3515625 Combine like terms: -0.3515625 + 0.3515625 = 0.0000000 0.0000000 + x = -0.080054303 + 0.3515625 x = -0.080054303 + 0.3515625 Combine like terms: -0.080054303 + 0.3515625 = 0.271508197 x = 0.271508197 Simplifying x = 0.271508197Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.431616803, 0.271508197}
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