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Simplifying 5x + 35 + 3x2 = 512 Reorder the terms: 35 + 5x + 3x2 = 512 Solving 35 + 5x + 3x2 = 512 Solving for variable 'x'. Reorder the terms: 35 + -512 + 5x + 3x2 = 512 + -512 Combine like terms: 35 + -512 = -477 -477 + 5x + 3x2 = 512 + -512 Combine like terms: 512 + -512 = 0 -477 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -159 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '159' to each side of the equation. -159 + 1.666666667x + 159 + x2 = 0 + 159 Reorder the terms: -159 + 159 + 1.666666667x + x2 = 0 + 159 Combine like terms: -159 + 159 = 0 0 + 1.666666667x + x2 = 0 + 159 1.666666667x + x2 = 0 + 159 Combine like terms: 0 + 159 = 159 1.666666667x + x2 = 159 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 159 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 159 + 0.6944444447 Combine like terms: 159 + 0.6944444447 = 159.6944444447 0.6944444447 + 1.666666667x + x2 = 159.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 159.6944444447 Calculate the square root of the right side: 12.637026725 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 12.637026725 and -12.637026725.Subproblem 1
x + 0.8333333335 = 12.637026725 Simplifying x + 0.8333333335 = 12.637026725 Reorder the terms: 0.8333333335 + x = 12.637026725 Solving 0.8333333335 + x = 12.637026725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 12.637026725 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 12.637026725 + -0.8333333335 x = 12.637026725 + -0.8333333335 Combine like terms: 12.637026725 + -0.8333333335 = 11.8036933915 x = 11.8036933915 Simplifying x = 11.8036933915Subproblem 2
x + 0.8333333335 = -12.637026725 Simplifying x + 0.8333333335 = -12.637026725 Reorder the terms: 0.8333333335 + x = -12.637026725 Solving 0.8333333335 + x = -12.637026725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -12.637026725 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -12.637026725 + -0.8333333335 x = -12.637026725 + -0.8333333335 Combine like terms: -12.637026725 + -0.8333333335 = -13.4703600585 x = -13.4703600585 Simplifying x = -13.4703600585Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.8036933915, -13.4703600585}
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