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Simplifying 8x2 + -30x = 10 Reorder the terms: -30x + 8x2 = 10 Solving -30x + 8x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -30x + 8x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -30x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -15x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -15x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + -15x + 4x2 = 0 Solving -5 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -3.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3.75x + x2 = 0 + 1.25 -3.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3.75x + x2 = 1.25 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 1.25 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 1.25 + 3.515625 Combine like terms: 1.25 + 3.515625 = 4.765625 3.515625 + -3.75x + x2 = 4.765625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (x + -1.875) equal to 2.18303115 and -2.18303115.Subproblem 1
x + -1.875 = 2.18303115 Simplifying x + -1.875 = 2.18303115 Reorder the terms: -1.875 + x = 2.18303115 Solving -1.875 + x = 2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.18303115 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.18303115 + 1.875 x = 2.18303115 + 1.875 Combine like terms: 2.18303115 + 1.875 = 4.05803115 x = 4.05803115 Simplifying x = 4.05803115Subproblem 2
x + -1.875 = -2.18303115 Simplifying x + -1.875 = -2.18303115 Reorder the terms: -1.875 + x = -2.18303115 Solving -1.875 + x = -2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.18303115 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.18303115 + 1.875 x = -2.18303115 + 1.875 Combine like terms: -2.18303115 + 1.875 = -0.30803115 x = -0.30803115 Simplifying x = -0.30803115Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05803115, -0.30803115}Solution
x = {4.05803115, -0.30803115}
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