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Simplifying 3x2 + 5x + 8 = 180 Reorder the terms: 8 + 5x + 3x2 = 180 Solving 8 + 5x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 8 + -180 + 5x + 3x2 = 180 + -180 Combine like terms: 8 + -180 = -172 -172 + 5x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -172 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -57.33333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '57.33333333' to each side of the equation. -57.33333333 + 1.666666667x + 57.33333333 + x2 = 0 + 57.33333333 Reorder the terms: -57.33333333 + 57.33333333 + 1.666666667x + x2 = 0 + 57.33333333 Combine like terms: -57.33333333 + 57.33333333 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 57.33333333 1.666666667x + x2 = 0 + 57.33333333 Combine like terms: 0 + 57.33333333 = 57.33333333 1.666666667x + x2 = 57.33333333 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 = 57.33333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 57.33333333 + 0.6944444447 Combine like terms: 57.33333333 + 0.6944444447 = 58.0277777747 0.6944444447 + 1.666666667x + x2 = 58.0277777747 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 58.0277777747 Calculate the square root of the right side: 7.617596588 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 7.617596588 and -7.617596588.Subproblem 1
x + 0.8333333335 = 7.617596588 Simplifying x + 0.8333333335 = 7.617596588 Reorder the terms: 0.8333333335 + x = 7.617596588 Solving 0.8333333335 + x = 7.617596588 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 = 7.617596588 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 7.617596588 + -0.8333333335 x = 7.617596588 + -0.8333333335 Combine like terms: 7.617596588 + -0.8333333335 = 6.7842632545 x = 6.7842632545 Simplifying x = 6.7842632545Subproblem 2
x + 0.8333333335 = -7.617596588 Simplifying x + 0.8333333335 = -7.617596588 Reorder the terms: 0.8333333335 + x = -7.617596588 Solving 0.8333333335 + x = -7.617596588 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 = -7.617596588 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -7.617596588 + -0.8333333335 x = -7.617596588 + -0.8333333335 Combine like terms: -7.617596588 + -0.8333333335 = -8.4509299215 x = -8.4509299215 Simplifying x = -8.4509299215Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.7842632545, -8.4509299215}
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