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Simplifying 14x2 + -24x + -48 = 0 Reorder the terms: -48 + -24x + 14x2 = 0 Solving -48 + -24x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -12x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -12x + 7x2)' equal to zero and attempt to solve: Simplifying -24 + -12x + 7x2 = 0 Solving -24 + -12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -1.714285714x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -1.714285714x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -1.714285714x + x2 = 0 + 3.428571429 -1.714285714x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -1.714285714x + x2 = 3.428571429 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = 3.428571429 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 3.428571429 + 0.7346938773 Combine like terms: 3.428571429 + 0.7346938773 = 4.1632653063 0.7346938773 + -1.714285714x + x2 = 4.1632653063 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 4.1632653063 Calculate the square root of the right side: 2.040408122 Break this problem into two subproblems by setting (x + -0.857142857) equal to 2.040408122 and -2.040408122.Subproblem 1
x + -0.857142857 = 2.040408122 Simplifying x + -0.857142857 = 2.040408122 Reorder the terms: -0.857142857 + x = 2.040408122 Solving -0.857142857 + x = 2.040408122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 2.040408122 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 2.040408122 + 0.857142857 x = 2.040408122 + 0.857142857 Combine like terms: 2.040408122 + 0.857142857 = 2.897550979 x = 2.897550979 Simplifying x = 2.897550979Subproblem 2
x + -0.857142857 = -2.040408122 Simplifying x + -0.857142857 = -2.040408122 Reorder the terms: -0.857142857 + x = -2.040408122 Solving -0.857142857 + x = -2.040408122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -2.040408122 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -2.040408122 + 0.857142857 x = -2.040408122 + 0.857142857 Combine like terms: -2.040408122 + 0.857142857 = -1.183265265 x = -1.183265265 Simplifying x = -1.183265265Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.897550979, -1.183265265}Solution
x = {2.897550979, -1.183265265}
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