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Simplifying 30x2 + -87x + -30 = 0 Reorder the terms: -30 + -87x + 30x2 = 0 Solving -30 + -87x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -29x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -29x + 10x2)' equal to zero and attempt to solve: Simplifying -10 + -29x + 10x2 = 0 Solving -10 + -29x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1 + -2.9x + x2 = 0.0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.9x + 1 + x2 = 0.0 + 1 Reorder the terms: -1 + 1 + -2.9x + x2 = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.9x + x2 = 0.0 + 1 -2.9x + x2 = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 -2.9x + x2 = 1 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = 1 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = 1 + 2.1025 Combine like terms: 1 + 2.1025 = 3.1025 2.1025 + -2.9x + x2 = 3.1025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 3.1025 Calculate the square root of the right side: 1.761391495 Break this problem into two subproblems by setting (x + -1.45) equal to 1.761391495 and -1.761391495.Subproblem 1
x + -1.45 = 1.761391495 Simplifying x + -1.45 = 1.761391495 Reorder the terms: -1.45 + x = 1.761391495 Solving -1.45 + x = 1.761391495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 1.761391495 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 1.761391495 + 1.45 x = 1.761391495 + 1.45 Combine like terms: 1.761391495 + 1.45 = 3.211391495 x = 3.211391495 Simplifying x = 3.211391495Subproblem 2
x + -1.45 = -1.761391495 Simplifying x + -1.45 = -1.761391495 Reorder the terms: -1.45 + x = -1.761391495 Solving -1.45 + x = -1.761391495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -1.761391495 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -1.761391495 + 1.45 x = -1.761391495 + 1.45 Combine like terms: -1.761391495 + 1.45 = -0.311391495 x = -0.311391495 Simplifying x = -0.311391495Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.211391495, -0.311391495}Solution
x = {3.211391495, -0.311391495}
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