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Simplifying -14 = 8x(6x + -17) Reorder the terms: -14 = 8x(-17 + 6x) -14 = (-17 * 8x + 6x * 8x) -14 = (-136x + 48x2) Solving -14 = -136x + 48x2 Solving for variable 'x'. Reorder the terms: -14 + 136x + -48x2 = -136x + 136x + 48x2 + -48x2 Combine like terms: -136x + 136x = 0 -14 + 136x + -48x2 = 0 + 48x2 + -48x2 -14 + 136x + -48x2 = 48x2 + -48x2 Combine like terms: 48x2 + -48x2 = 0 -14 + 136x + -48x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 68x + -24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 68x + -24x2)' equal to zero and attempt to solve: Simplifying -7 + 68x + -24x2 = 0 Solving -7 + 68x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 0.2916666667 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '-0.2916666667' to each side of the equation. 0.2916666667 + -2.833333333x + -0.2916666667 + x2 = 0 + -0.2916666667 Reorder the terms: 0.2916666667 + -0.2916666667 + -2.833333333x + x2 = 0 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + -2.833333333x + x2 = 0 + -0.2916666667 -2.833333333x + x2 = 0 + -0.2916666667 Combine like terms: 0 + -0.2916666667 = -0.2916666667 -2.833333333x + x2 = -0.2916666667 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = -0.2916666667 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = -0.2916666667 + 2.006944445 Combine like terms: -0.2916666667 + 2.006944445 = 1.7152777783 2.006944445 + -2.833333333x + x2 = 1.7152777783 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 1.7152777783 Calculate the square root of the right side: 1.309686137 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.309686137 and -1.309686137.Subproblem 1
x + -1.416666667 = 1.309686137 Simplifying x + -1.416666667 = 1.309686137 Reorder the terms: -1.416666667 + x = 1.309686137 Solving -1.416666667 + x = 1.309686137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 1.309686137 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.309686137 + 1.416666667 x = 1.309686137 + 1.416666667 Combine like terms: 1.309686137 + 1.416666667 = 2.726352804 x = 2.726352804 Simplifying x = 2.726352804Subproblem 2
x + -1.416666667 = -1.309686137 Simplifying x + -1.416666667 = -1.309686137 Reorder the terms: -1.416666667 + x = -1.309686137 Solving -1.416666667 + x = -1.309686137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -1.309686137 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.309686137 + 1.416666667 x = -1.309686137 + 1.416666667 Combine like terms: -1.309686137 + 1.416666667 = 0.10698053 x = 0.10698053 Simplifying x = 0.10698053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.726352804, 0.10698053}Solution
x = {2.726352804, 0.10698053}
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