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Simplifying 2x + 15 = 36x2 Reorder the terms: 15 + 2x = 36x2 Solving 15 + 2x = 36x2 Solving for variable 'x'. Combine like terms: 36x2 + -36x2 = 0 15 + 2x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -0.4166666667 + -0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.05555555556x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.05555555556x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.05555555556x + x2 = 0 + 0.4166666667 -0.05555555556x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.05555555556x + x2 = 0.4166666667 The x term is -0.05555555556x. Take half its coefficient (-0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. -0.05555555556x + 0.0007716049384 + x2 = 0.4166666667 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556x + x2 = 0.4166666667 + 0.0007716049384 Combine like terms: 0.4166666667 + 0.0007716049384 = 0.4174382716384 0.0007716049384 + -0.05555555556x + x2 = 0.4174382716384 Factor a perfect square on the left side: (x + -0.02777777778)(x + -0.02777777778) = 0.4174382716384 Calculate the square root of the right side: 0.646094631 Break this problem into two subproblems by setting (x + -0.02777777778) equal to 0.646094631 and -0.646094631.Subproblem 1
x + -0.02777777778 = 0.646094631 Simplifying x + -0.02777777778 = 0.646094631 Reorder the terms: -0.02777777778 + x = 0.646094631 Solving -0.02777777778 + x = 0.646094631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = 0.646094631 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = 0.646094631 + 0.02777777778 x = 0.646094631 + 0.02777777778 Combine like terms: 0.646094631 + 0.02777777778 = 0.67387240878 x = 0.67387240878 Simplifying x = 0.67387240878Subproblem 2
x + -0.02777777778 = -0.646094631 Simplifying x + -0.02777777778 = -0.646094631 Reorder the terms: -0.02777777778 + x = -0.646094631 Solving -0.02777777778 + x = -0.646094631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = -0.646094631 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = -0.646094631 + 0.02777777778 x = -0.646094631 + 0.02777777778 Combine like terms: -0.646094631 + 0.02777777778 = -0.61831685322 x = -0.61831685322 Simplifying x = -0.61831685322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67387240878, -0.61831685322}
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