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Simplifying 6x2 + -10x + -154 = 0 Reorder the terms: -154 + -10x + 6x2 = 0 Solving -154 + -10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-77 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-77 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -77 + -5x + 3x2 = 0 Solving -77 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.66666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '25.66666667' to each side of the equation. -25.66666667 + -1.666666667x + 25.66666667 + x2 = 0 + 25.66666667 Reorder the terms: -25.66666667 + 25.66666667 + -1.666666667x + x2 = 0 + 25.66666667 Combine like terms: -25.66666667 + 25.66666667 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 25.66666667 -1.666666667x + x2 = 0 + 25.66666667 Combine like terms: 0 + 25.66666667 = 25.66666667 -1.666666667x + x2 = 25.66666667 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 = 25.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 25.66666667 + 0.6944444447 Combine like terms: 25.66666667 + 0.6944444447 = 26.3611111147 0.6944444447 + -1.666666667x + x2 = 26.3611111147 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 26.3611111147 Calculate the square root of the right side: 5.134307267 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 5.134307267 and -5.134307267.Subproblem 1
x + -0.8333333335 = 5.134307267 Simplifying x + -0.8333333335 = 5.134307267 Reorder the terms: -0.8333333335 + x = 5.134307267 Solving -0.8333333335 + x = 5.134307267 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 = 5.134307267 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 5.134307267 + 0.8333333335 x = 5.134307267 + 0.8333333335 Combine like terms: 5.134307267 + 0.8333333335 = 5.9676406005 x = 5.9676406005 Simplifying x = 5.9676406005Subproblem 2
x + -0.8333333335 = -5.134307267 Simplifying x + -0.8333333335 = -5.134307267 Reorder the terms: -0.8333333335 + x = -5.134307267 Solving -0.8333333335 + x = -5.134307267 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 = -5.134307267 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -5.134307267 + 0.8333333335 x = -5.134307267 + 0.8333333335 Combine like terms: -5.134307267 + 0.8333333335 = -4.3009739335 x = -4.3009739335 Simplifying x = -4.3009739335Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.9676406005, -4.3009739335}Solution
x = {5.9676406005, -4.3009739335}
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