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Simplifying 232x2 + -235 = 89x Reorder the terms: -235 + 232x2 = 89x Solving -235 + 232x2 = 89x Solving for variable 'x'. Reorder the terms: -235 + -89x + 232x2 = 89x + -89x Combine like terms: 89x + -89x = 0 -235 + -89x + 232x2 = 0 Begin completing the square. Divide all terms by 232 the coefficient of the squared term: Divide each side by '232'. -1.012931034 + -0.3836206897x + x2 = 0 Move the constant term to the right: Add '1.012931034' to each side of the equation. -1.012931034 + -0.3836206897x + 1.012931034 + x2 = 0 + 1.012931034 Reorder the terms: -1.012931034 + 1.012931034 + -0.3836206897x + x2 = 0 + 1.012931034 Combine like terms: -1.012931034 + 1.012931034 = 0.000000000 0.000000000 + -0.3836206897x + x2 = 0 + 1.012931034 -0.3836206897x + x2 = 0 + 1.012931034 Combine like terms: 0 + 1.012931034 = 1.012931034 -0.3836206897x + x2 = 1.012931034 The x term is -0.3836206897x. Take half its coefficient (-0.1918103449). Square it (0.03679120841) and add it to both sides. Add '0.03679120841' to each side of the equation. -0.3836206897x + 0.03679120841 + x2 = 1.012931034 + 0.03679120841 Reorder the terms: 0.03679120841 + -0.3836206897x + x2 = 1.012931034 + 0.03679120841 Combine like terms: 1.012931034 + 0.03679120841 = 1.04972224241 0.03679120841 + -0.3836206897x + x2 = 1.04972224241 Factor a perfect square on the left side: (x + -0.1918103449)(x + -0.1918103449) = 1.04972224241 Calculate the square root of the right side: 1.024559536 Break this problem into two subproblems by setting (x + -0.1918103449) equal to 1.024559536 and -1.024559536.Subproblem 1
x + -0.1918103449 = 1.024559536 Simplifying x + -0.1918103449 = 1.024559536 Reorder the terms: -0.1918103449 + x = 1.024559536 Solving -0.1918103449 + x = 1.024559536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1918103449' to each side of the equation. -0.1918103449 + 0.1918103449 + x = 1.024559536 + 0.1918103449 Combine like terms: -0.1918103449 + 0.1918103449 = 0.0000000000 0.0000000000 + x = 1.024559536 + 0.1918103449 x = 1.024559536 + 0.1918103449 Combine like terms: 1.024559536 + 0.1918103449 = 1.2163698809 x = 1.2163698809 Simplifying x = 1.2163698809Subproblem 2
x + -0.1918103449 = -1.024559536 Simplifying x + -0.1918103449 = -1.024559536 Reorder the terms: -0.1918103449 + x = -1.024559536 Solving -0.1918103449 + x = -1.024559536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1918103449' to each side of the equation. -0.1918103449 + 0.1918103449 + x = -1.024559536 + 0.1918103449 Combine like terms: -0.1918103449 + 0.1918103449 = 0.0000000000 0.0000000000 + x = -1.024559536 + 0.1918103449 x = -1.024559536 + 0.1918103449 Combine like terms: -1.024559536 + 0.1918103449 = -0.8327491911 x = -0.8327491911 Simplifying x = -0.8327491911Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2163698809, -0.8327491911}
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