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Simplifying 2x(3x + -5) = 90 Reorder the terms: 2x(-5 + 3x) = 90 (-5 * 2x + 3x * 2x) = 90 (-10x + 6x2) = 90 Solving -10x + 6x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -10x + 6x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -45 + -5x + 3x2 = 0 Solving -45 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -1.666666667x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -1.666666667x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1.666666667x + x2 = 0 + 15 -1.666666667x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1.666666667x + x2 = 15 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 = 15 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 15 + 0.6944444447 Combine like terms: 15 + 0.6944444447 = 15.6944444447 0.6944444447 + -1.666666667x + x2 = 15.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 15.6944444447 Calculate the square root of the right side: 3.961621441 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 3.961621441 and -3.961621441.Subproblem 1
x + -0.8333333335 = 3.961621441 Simplifying x + -0.8333333335 = 3.961621441 Reorder the terms: -0.8333333335 + x = 3.961621441 Solving -0.8333333335 + x = 3.961621441 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 = 3.961621441 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 3.961621441 + 0.8333333335 x = 3.961621441 + 0.8333333335 Combine like terms: 3.961621441 + 0.8333333335 = 4.7949547745 x = 4.7949547745 Simplifying x = 4.7949547745Subproblem 2
x + -0.8333333335 = -3.961621441 Simplifying x + -0.8333333335 = -3.961621441 Reorder the terms: -0.8333333335 + x = -3.961621441 Solving -0.8333333335 + x = -3.961621441 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 = -3.961621441 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -3.961621441 + 0.8333333335 x = -3.961621441 + 0.8333333335 Combine like terms: -3.961621441 + 0.8333333335 = -3.1282881075 x = -3.1282881075 Simplifying x = -3.1282881075Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7949547745, -3.1282881075}Solution
x = {4.7949547745, -3.1282881075}
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