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Simplifying 14x2 + -14x + -30 = 0 Reorder the terms: -30 + -14x + 14x2 = 0 Solving -30 + -14x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -7x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -7x + 7x2)' equal to zero and attempt to solve: Simplifying -15 + -7x + 7x2 = 0 Solving -15 + -7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + -1x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -1x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -1x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -1x + x2 = 0 + 2.142857143 -1x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -1x + x2 = 2.142857143 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.142857143 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.142857143 + 0.25 Combine like terms: 2.142857143 + 0.25 = 2.392857143 0.25 + -1x + x2 = 2.392857143 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.392857143 Calculate the square root of the right side: 1.546886273 Break this problem into two subproblems by setting (x + -0.5) equal to 1.546886273 and -1.546886273.Subproblem 1
x + -0.5 = 1.546886273 Simplifying x + -0.5 = 1.546886273 Reorder the terms: -0.5 + x = 1.546886273 Solving -0.5 + x = 1.546886273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.546886273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.546886273 + 0.5 x = 1.546886273 + 0.5 Combine like terms: 1.546886273 + 0.5 = 2.046886273 x = 2.046886273 Simplifying x = 2.046886273Subproblem 2
x + -0.5 = -1.546886273 Simplifying x + -0.5 = -1.546886273 Reorder the terms: -0.5 + x = -1.546886273 Solving -0.5 + x = -1.546886273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.546886273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.546886273 + 0.5 x = -1.546886273 + 0.5 Combine like terms: -1.546886273 + 0.5 = -1.046886273 x = -1.046886273 Simplifying x = -1.046886273Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.046886273, -1.046886273}Solution
x = {2.046886273, -1.046886273}
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