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Simplifying 6x2 + 28x + -8 = 0 Reorder the terms: -8 + 28x + 6x2 = 0 Solving -8 + 28x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 14x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + 14x + 3x2 = 0 Solving -4 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 4.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 4.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + 1.333333333 4.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 4.666666667x + x2 = 1.333333333 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 1.333333333 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 1.333333333 + 5.444444448 Combine like terms: 1.333333333 + 5.444444448 = 6.777777781 5.444444448 + 4.666666667x + x2 = 6.777777781 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 6.777777781 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (x + 2.333333334) equal to 2.603416559 and -2.603416559.Subproblem 1
x + 2.333333334 = 2.603416559 Simplifying x + 2.333333334 = 2.603416559 Reorder the terms: 2.333333334 + x = 2.603416559 Solving 2.333333334 + x = 2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 2.603416559 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.603416559 + -2.333333334 x = 2.603416559 + -2.333333334 Combine like terms: 2.603416559 + -2.333333334 = 0.270083225 x = 0.270083225 Simplifying x = 0.270083225Subproblem 2
x + 2.333333334 = -2.603416559 Simplifying x + 2.333333334 = -2.603416559 Reorder the terms: 2.333333334 + x = -2.603416559 Solving 2.333333334 + x = -2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -2.603416559 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.603416559 + -2.333333334 x = -2.603416559 + -2.333333334 Combine like terms: -2.603416559 + -2.333333334 = -4.936749893 x = -4.936749893 Simplifying x = -4.936749893Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.270083225, -4.936749893}Solution
x = {0.270083225, -4.936749893}
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