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Simplifying -28x2 + -186x + -96 = 0 Reorder the terms: -96 + -186x + -28x2 = 0 Solving -96 + -186x + -28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(48 + 93x + 14x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(48 + 93x + 14x2)' equal to zero and attempt to solve: Simplifying 48 + 93x + 14x2 = 0 Solving 48 + 93x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 3.428571429 + 6.642857143x + x2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + 6.642857143x + -3.428571429 + x2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + 6.642857143x + x2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + 6.642857143x + x2 = 0 + -3.428571429 6.642857143x + x2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 6.642857143x + x2 = -3.428571429 The x term is 6.642857143x. Take half its coefficient (3.321428572). Square it (11.03188776) and add it to both sides. Add '11.03188776' to each side of the equation. 6.642857143x + 11.03188776 + x2 = -3.428571429 + 11.03188776 Reorder the terms: 11.03188776 + 6.642857143x + x2 = -3.428571429 + 11.03188776 Combine like terms: -3.428571429 + 11.03188776 = 7.603316331 11.03188776 + 6.642857143x + x2 = 7.603316331 Factor a perfect square on the left side: (x + 3.321428572)(x + 3.321428572) = 7.603316331 Calculate the square root of the right side: 2.757411165 Break this problem into two subproblems by setting (x + 3.321428572) equal to 2.757411165 and -2.757411165.Subproblem 1
x + 3.321428572 = 2.757411165 Simplifying x + 3.321428572 = 2.757411165 Reorder the terms: 3.321428572 + x = 2.757411165 Solving 3.321428572 + x = 2.757411165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.321428572' to each side of the equation. 3.321428572 + -3.321428572 + x = 2.757411165 + -3.321428572 Combine like terms: 3.321428572 + -3.321428572 = 0.000000000 0.000000000 + x = 2.757411165 + -3.321428572 x = 2.757411165 + -3.321428572 Combine like terms: 2.757411165 + -3.321428572 = -0.564017407 x = -0.564017407 Simplifying x = -0.564017407Subproblem 2
x + 3.321428572 = -2.757411165 Simplifying x + 3.321428572 = -2.757411165 Reorder the terms: 3.321428572 + x = -2.757411165 Solving 3.321428572 + x = -2.757411165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.321428572' to each side of the equation. 3.321428572 + -3.321428572 + x = -2.757411165 + -3.321428572 Combine like terms: 3.321428572 + -3.321428572 = 0.000000000 0.000000000 + x = -2.757411165 + -3.321428572 x = -2.757411165 + -3.321428572 Combine like terms: -2.757411165 + -3.321428572 = -6.078839737 x = -6.078839737 Simplifying x = -6.078839737Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.564017407, -6.078839737}Solution
x = {-0.564017407, -6.078839737}
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