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Simplifying -51x2 + 11x + 6 = 0 Reorder the terms: 6 + 11x + -51x2 = 0 Solving 6 + 11x + -51x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -51 the coefficient of the squared term: Divide each side by '-51'. -0.1176470588 + -0.2156862745x + x2 = 0 Move the constant term to the right: Add '0.1176470588' to each side of the equation. -0.1176470588 + -0.2156862745x + 0.1176470588 + x2 = 0 + 0.1176470588 Reorder the terms: -0.1176470588 + 0.1176470588 + -0.2156862745x + x2 = 0 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + -0.2156862745x + x2 = 0 + 0.1176470588 -0.2156862745x + x2 = 0 + 0.1176470588 Combine like terms: 0 + 0.1176470588 = 0.1176470588 -0.2156862745x + x2 = 0.1176470588 The x term is -0.2156862745x. Take half its coefficient (-0.1078431373). Square it (0.01163014226) and add it to both sides. Add '0.01163014226' to each side of the equation. -0.2156862745x + 0.01163014226 + x2 = 0.1176470588 + 0.01163014226 Reorder the terms: 0.01163014226 + -0.2156862745x + x2 = 0.1176470588 + 0.01163014226 Combine like terms: 0.1176470588 + 0.01163014226 = 0.12927720106 0.01163014226 + -0.2156862745x + x2 = 0.12927720106 Factor a perfect square on the left side: (x + -0.1078431373)(x + -0.1078431373) = 0.12927720106 Calculate the square root of the right side: 0.359551389 Break this problem into two subproblems by setting (x + -0.1078431373) equal to 0.359551389 and -0.359551389.Subproblem 1
x + -0.1078431373 = 0.359551389 Simplifying x + -0.1078431373 = 0.359551389 Reorder the terms: -0.1078431373 + x = 0.359551389 Solving -0.1078431373 + x = 0.359551389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1078431373' to each side of the equation. -0.1078431373 + 0.1078431373 + x = 0.359551389 + 0.1078431373 Combine like terms: -0.1078431373 + 0.1078431373 = 0.0000000000 0.0000000000 + x = 0.359551389 + 0.1078431373 x = 0.359551389 + 0.1078431373 Combine like terms: 0.359551389 + 0.1078431373 = 0.4673945263 x = 0.4673945263 Simplifying x = 0.4673945263Subproblem 2
x + -0.1078431373 = -0.359551389 Simplifying x + -0.1078431373 = -0.359551389 Reorder the terms: -0.1078431373 + x = -0.359551389 Solving -0.1078431373 + x = -0.359551389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1078431373' to each side of the equation. -0.1078431373 + 0.1078431373 + x = -0.359551389 + 0.1078431373 Combine like terms: -0.1078431373 + 0.1078431373 = 0.0000000000 0.0000000000 + x = -0.359551389 + 0.1078431373 x = -0.359551389 + 0.1078431373 Combine like terms: -0.359551389 + 0.1078431373 = -0.2517082517 x = -0.2517082517 Simplifying x = -0.2517082517Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4673945263, -0.2517082517}
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