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Simplifying 10x2 + 20x + -30 = 8 Reorder the terms: -30 + 20x + 10x2 = 8 Solving -30 + 20x + 10x2 = 8 Solving for variable 'x'. Reorder the terms: -30 + -8 + 20x + 10x2 = 8 + -8 Combine like terms: -30 + -8 = -38 -38 + 20x + 10x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -38 + 20x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 10x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 10x + 5x2)' equal to zero and attempt to solve: Simplifying -19 + 10x + 5x2 = 0 Solving -19 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + 2x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 2x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 2x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 2x + x2 = 0 + 3.8 2x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 2x + x2 = 3.8 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 3.8 + 1 Reorder the terms: 1 + 2x + x2 = 3.8 + 1 Combine like terms: 3.8 + 1 = 4.8 1 + 2x + x2 = 4.8 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.8 Calculate the square root of the right side: 2.19089023 Break this problem into two subproblems by setting (x + 1) equal to 2.19089023 and -2.19089023.Subproblem 1
x + 1 = 2.19089023 Simplifying x + 1 = 2.19089023 Reorder the terms: 1 + x = 2.19089023 Solving 1 + x = 2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.19089023 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.19089023 + -1 x = 2.19089023 + -1 Combine like terms: 2.19089023 + -1 = 1.19089023 x = 1.19089023 Simplifying x = 1.19089023Subproblem 2
x + 1 = -2.19089023 Simplifying x + 1 = -2.19089023 Reorder the terms: 1 + x = -2.19089023 Solving 1 + x = -2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.19089023 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.19089023 + -1 x = -2.19089023 + -1 Combine like terms: -2.19089023 + -1 = -3.19089023 x = -3.19089023 Simplifying x = -3.19089023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.19089023, -3.19089023}Solution
x = {1.19089023, -3.19089023}
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