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Simplifying 14x2 + -72x + -64 = 0 Reorder the terms: -64 + -72x + 14x2 = 0 Solving -64 + -72x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + -36x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + -36x + 7x2)' equal to zero and attempt to solve: Simplifying -32 + -36x + 7x2 = 0 Solving -32 + -36x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.571428571 + -5.142857143x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + -5.142857143x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + -5.142857143x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + -5.142857143x + x2 = 0 + 4.571428571 -5.142857143x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 -5.142857143x + x2 = 4.571428571 The x term is -5.142857143x. Take half its coefficient (-2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. -5.142857143x + 6.612244901 + x2 = 4.571428571 + 6.612244901 Reorder the terms: 6.612244901 + -5.142857143x + x2 = 4.571428571 + 6.612244901 Combine like terms: 4.571428571 + 6.612244901 = 11.183673472 6.612244901 + -5.142857143x + x2 = 11.183673472 Factor a perfect square on the left side: (x + -2.571428572)(x + -2.571428572) = 11.183673472 Calculate the square root of the right side: 3.344199975 Break this problem into two subproblems by setting (x + -2.571428572) equal to 3.344199975 and -3.344199975.Subproblem 1
x + -2.571428572 = 3.344199975 Simplifying x + -2.571428572 = 3.344199975 Reorder the terms: -2.571428572 + x = 3.344199975 Solving -2.571428572 + x = 3.344199975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.571428572' to each side of the equation. -2.571428572 + 2.571428572 + x = 3.344199975 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = 3.344199975 + 2.571428572 x = 3.344199975 + 2.571428572 Combine like terms: 3.344199975 + 2.571428572 = 5.915628547 x = 5.915628547 Simplifying x = 5.915628547Subproblem 2
x + -2.571428572 = -3.344199975 Simplifying x + -2.571428572 = -3.344199975 Reorder the terms: -2.571428572 + x = -3.344199975 Solving -2.571428572 + x = -3.344199975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.571428572' to each side of the equation. -2.571428572 + 2.571428572 + x = -3.344199975 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = -3.344199975 + 2.571428572 x = -3.344199975 + 2.571428572 Combine like terms: -3.344199975 + 2.571428572 = -0.772771403 x = -0.772771403 Simplifying x = -0.772771403Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.915628547, -0.772771403}Solution
x = {5.915628547, -0.772771403}
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