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Simplifying -14x2 + 60x + 10 = 0 Reorder the terms: 10 + 60x + -14x2 = 0 Solving 10 + 60x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 30x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 30x + -7x2)' equal to zero and attempt to solve: Simplifying 5 + 30x + -7x2 = 0 Solving 5 + 30x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.7142857143 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -4.285714286x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -4.285714286x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -4.285714286x + x2 = 0 + 0.7142857143 -4.285714286x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -4.285714286x + x2 = 0.7142857143 The x term is -4.285714286x. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286x + 4.591836735 + x2 = 0.7142857143 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = 0.7142857143 + 4.591836735 Combine like terms: 0.7142857143 + 4.591836735 = 5.3061224493 4.591836735 + -4.285714286x + x2 = 5.3061224493 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 5.3061224493 Calculate the square root of the right side: 2.303502214 Break this problem into two subproblems by setting (x + -2.142857143) equal to 2.303502214 and -2.303502214.Subproblem 1
x + -2.142857143 = 2.303502214 Simplifying x + -2.142857143 = 2.303502214 Reorder the terms: -2.142857143 + x = 2.303502214 Solving -2.142857143 + x = 2.303502214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = 2.303502214 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 2.303502214 + 2.142857143 x = 2.303502214 + 2.142857143 Combine like terms: 2.303502214 + 2.142857143 = 4.446359357 x = 4.446359357 Simplifying x = 4.446359357Subproblem 2
x + -2.142857143 = -2.303502214 Simplifying x + -2.142857143 = -2.303502214 Reorder the terms: -2.142857143 + x = -2.303502214 Solving -2.142857143 + x = -2.303502214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = -2.303502214 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -2.303502214 + 2.142857143 x = -2.303502214 + 2.142857143 Combine like terms: -2.303502214 + 2.142857143 = -0.160645071 x = -0.160645071 Simplifying x = -0.160645071Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.446359357, -0.160645071}Solution
x = {4.446359357, -0.160645071}
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