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Simplifying 36x2 + 2x = 63 Reorder the terms: 2x + 36x2 = 63 Solving 2x + 36x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 2x + 36x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 2x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.75 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.05555555556x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.05555555556x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.05555555556x + x2 = 0 + 1.75 0.05555555556x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.05555555556x + x2 = 1.75 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 = 1.75 + 0.0007716049384 Reorder the terms: 0.0007716049384 + 0.05555555556x + x2 = 1.75 + 0.0007716049384 Combine like terms: 1.75 + 0.0007716049384 = 1.7507716049384 0.0007716049384 + 0.05555555556x + x2 = 1.7507716049384 Factor a perfect square on the left side: (x + 0.02777777778)(x + 0.02777777778) = 1.7507716049384 Calculate the square root of the right side: 1.323167263 Break this problem into two subproblems by setting (x + 0.02777777778) equal to 1.323167263 and -1.323167263.Subproblem 1
x + 0.02777777778 = 1.323167263 Simplifying x + 0.02777777778 = 1.323167263 Reorder the terms: 0.02777777778 + x = 1.323167263 Solving 0.02777777778 + x = 1.323167263 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 = 1.323167263 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = 1.323167263 + -0.02777777778 x = 1.323167263 + -0.02777777778 Combine like terms: 1.323167263 + -0.02777777778 = 1.29538948522 x = 1.29538948522 Simplifying x = 1.29538948522Subproblem 2
x + 0.02777777778 = -1.323167263 Simplifying x + 0.02777777778 = -1.323167263 Reorder the terms: 0.02777777778 + x = -1.323167263 Solving 0.02777777778 + x = -1.323167263 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 = -1.323167263 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = -1.323167263 + -0.02777777778 x = -1.323167263 + -0.02777777778 Combine like terms: -1.323167263 + -0.02777777778 = -1.35094504078 x = -1.35094504078 Simplifying x = -1.35094504078Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29538948522, -1.35094504078}
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