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Simplifying 15x2 + -78x + -15 = 0 Reorder the terms: -15 + -78x + 15x2 = 0 Solving -15 + -78x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -26x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -26x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + -26x + 5x2 = 0 Solving -5 + -26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -5.2x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5.2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -5.2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5.2x + x2 = 0 + 1 -5.2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5.2x + x2 = 1 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = 1 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 1 + 6.76 Combine like terms: 1 + 6.76 = 7.76 6.76 + -5.2x + x2 = 7.76 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 7.76 Calculate the square root of the right side: 2.785677655 Break this problem into two subproblems by setting (x + -2.6) equal to 2.785677655 and -2.785677655.Subproblem 1
x + -2.6 = 2.785677655 Simplifying x + -2.6 = 2.785677655 Reorder the terms: -2.6 + x = 2.785677655 Solving -2.6 + x = 2.785677655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 2.785677655 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 2.785677655 + 2.6 x = 2.785677655 + 2.6 Combine like terms: 2.785677655 + 2.6 = 5.385677655 x = 5.385677655 Simplifying x = 5.385677655Subproblem 2
x + -2.6 = -2.785677655 Simplifying x + -2.6 = -2.785677655 Reorder the terms: -2.6 + x = -2.785677655 Solving -2.6 + x = -2.785677655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -2.785677655 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -2.785677655 + 2.6 x = -2.785677655 + 2.6 Combine like terms: -2.785677655 + 2.6 = -0.185677655 x = -0.185677655 Simplifying x = -0.185677655Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.385677655, -0.185677655}Solution
x = {5.385677655, -0.185677655}
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