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Simplifying 140 = 6x2 + -10x Reorder the terms: 140 = -10x + 6x2 Solving 140 = -10x + 6x2 Solving for variable 'x'. Reorder the terms: 140 + 10x + -6x2 = -10x + 10x + 6x2 + -6x2 Combine like terms: -10x + 10x = 0 140 + 10x + -6x2 = 0 + 6x2 + -6x2 140 + 10x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 140 + 10x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(70 + 5x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(70 + 5x + -3x2)' equal to zero and attempt to solve: Simplifying 70 + 5x + -3x2 = 0 Solving 70 + 5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -23.33333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + -1.666666667x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + -1.666666667x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 23.33333333 -1.666666667x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 -1.666666667x + x2 = 23.33333333 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 = 23.33333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 23.33333333 + 0.6944444447 Combine like terms: 23.33333333 + 0.6944444447 = 24.0277777747 0.6944444447 + -1.666666667x + x2 = 24.0277777747 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 24.0277777747 Calculate the square root of the right side: 4.901813723 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 4.901813723 and -4.901813723.Subproblem 1
x + -0.8333333335 = 4.901813723 Simplifying x + -0.8333333335 = 4.901813723 Reorder the terms: -0.8333333335 + x = 4.901813723 Solving -0.8333333335 + x = 4.901813723 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 = 4.901813723 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 4.901813723 + 0.8333333335 x = 4.901813723 + 0.8333333335 Combine like terms: 4.901813723 + 0.8333333335 = 5.7351470565 x = 5.7351470565 Simplifying x = 5.7351470565Subproblem 2
x + -0.8333333335 = -4.901813723 Simplifying x + -0.8333333335 = -4.901813723 Reorder the terms: -0.8333333335 + x = -4.901813723 Solving -0.8333333335 + x = -4.901813723 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 = -4.901813723 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -4.901813723 + 0.8333333335 x = -4.901813723 + 0.8333333335 Combine like terms: -4.901813723 + 0.8333333335 = -4.0684803895 x = -4.0684803895 Simplifying x = -4.0684803895Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.7351470565, -4.0684803895}Solution
x = {5.7351470565, -4.0684803895}
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