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Simplifying 3x2 + -5x + -150 = 0 Reorder the terms: -150 + -5x + 3x2 = 0 Solving -150 + -5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -50 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -1.666666667x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -1.666666667x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -1.666666667x + x2 = 0 + 50 -1.666666667x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -1.666666667x + x2 = 50 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 = 50 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 50 + 0.6944444447 Combine like terms: 50 + 0.6944444447 = 50.6944444447 0.6944444447 + -1.666666667x + x2 = 50.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 50.6944444447 Calculate the square root of the right side: 7.120003121 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 7.120003121 and -7.120003121.Subproblem 1
x + -0.8333333335 = 7.120003121 Simplifying x + -0.8333333335 = 7.120003121 Reorder the terms: -0.8333333335 + x = 7.120003121 Solving -0.8333333335 + x = 7.120003121 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 = 7.120003121 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 7.120003121 + 0.8333333335 x = 7.120003121 + 0.8333333335 Combine like terms: 7.120003121 + 0.8333333335 = 7.9533364545 x = 7.9533364545 Simplifying x = 7.9533364545Subproblem 2
x + -0.8333333335 = -7.120003121 Simplifying x + -0.8333333335 = -7.120003121 Reorder the terms: -0.8333333335 + x = -7.120003121 Solving -0.8333333335 + x = -7.120003121 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 = -7.120003121 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -7.120003121 + 0.8333333335 x = -7.120003121 + 0.8333333335 Combine like terms: -7.120003121 + 0.8333333335 = -6.2866697875 x = -6.2866697875 Simplifying x = -6.2866697875Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.9533364545, -6.2866697875}
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