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Simplifying 12x2 + -176x + 259 = 0 Reorder the terms: 259 + -176x + 12x2 = 0 Solving 259 + -176x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 21.58333333 + -14.66666667x + x2 = 0 Move the constant term to the right: Add '-21.58333333' to each side of the equation. 21.58333333 + -14.66666667x + -21.58333333 + x2 = 0 + -21.58333333 Reorder the terms: 21.58333333 + -21.58333333 + -14.66666667x + x2 = 0 + -21.58333333 Combine like terms: 21.58333333 + -21.58333333 = 0.00000000 0.00000000 + -14.66666667x + x2 = 0 + -21.58333333 -14.66666667x + x2 = 0 + -21.58333333 Combine like terms: 0 + -21.58333333 = -21.58333333 -14.66666667x + x2 = -21.58333333 The x term is -14.66666667x. Take half its coefficient (-7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. -14.66666667x + 53.77777780 + x2 = -21.58333333 + 53.77777780 Reorder the terms: 53.77777780 + -14.66666667x + x2 = -21.58333333 + 53.77777780 Combine like terms: -21.58333333 + 53.77777780 = 32.19444447 53.77777780 + -14.66666667x + x2 = 32.19444447 Factor a perfect square on the left side: (x + -7.333333335)(x + -7.333333335) = 32.19444447 Calculate the square root of the right side: 5.674014846 Break this problem into two subproblems by setting (x + -7.333333335) equal to 5.674014846 and -5.674014846.Subproblem 1
x + -7.333333335 = 5.674014846 Simplifying x + -7.333333335 = 5.674014846 Reorder the terms: -7.333333335 + x = 5.674014846 Solving -7.333333335 + x = 5.674014846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + x = 5.674014846 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + x = 5.674014846 + 7.333333335 x = 5.674014846 + 7.333333335 Combine like terms: 5.674014846 + 7.333333335 = 13.007348181 x = 13.007348181 Simplifying x = 13.007348181Subproblem 2
x + -7.333333335 = -5.674014846 Simplifying x + -7.333333335 = -5.674014846 Reorder the terms: -7.333333335 + x = -5.674014846 Solving -7.333333335 + x = -5.674014846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + x = -5.674014846 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + x = -5.674014846 + 7.333333335 x = -5.674014846 + 7.333333335 Combine like terms: -5.674014846 + 7.333333335 = 1.659318489 x = 1.659318489 Simplifying x = 1.659318489Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.007348181, 1.659318489}
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