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Simplifying 18x2 + -63 = x Reorder the terms: -63 + 18x2 = x Solving -63 + 18x2 = x Solving for variable 'x'. Reorder the terms: -63 + -1x + 18x2 = x + -1x Combine like terms: x + -1x = 0 -63 + -1x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.5 + -0.05555555556x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.05555555556x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.05555555556x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.05555555556x + x2 = 0 + 3.5 -0.05555555556x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.05555555556x + x2 = 3.5 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 = 3.5 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556x + x2 = 3.5 + 0.0007716049384 Combine like terms: 3.5 + 0.0007716049384 = 3.5007716049384 0.0007716049384 + -0.05555555556x + x2 = 3.5007716049384 Factor a perfect square on the left side: (x + -0.02777777778)(x + -0.02777777778) = 3.5007716049384 Calculate the square root of the right side: 1.871034902 Break this problem into two subproblems by setting (x + -0.02777777778) equal to 1.871034902 and -1.871034902.Subproblem 1
x + -0.02777777778 = 1.871034902 Simplifying x + -0.02777777778 = 1.871034902 Reorder the terms: -0.02777777778 + x = 1.871034902 Solving -0.02777777778 + x = 1.871034902 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 = 1.871034902 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = 1.871034902 + 0.02777777778 x = 1.871034902 + 0.02777777778 Combine like terms: 1.871034902 + 0.02777777778 = 1.89881267978 x = 1.89881267978 Simplifying x = 1.89881267978Subproblem 2
x + -0.02777777778 = -1.871034902 Simplifying x + -0.02777777778 = -1.871034902 Reorder the terms: -0.02777777778 + x = -1.871034902 Solving -0.02777777778 + x = -1.871034902 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 = -1.871034902 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = -1.871034902 + 0.02777777778 x = -1.871034902 + 0.02777777778 Combine like terms: -1.871034902 + 0.02777777778 = -1.84325712422 x = -1.84325712422 Simplifying x = -1.84325712422Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.89881267978, -1.84325712422}
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