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Simplifying 10x2 + 20x + -18 = 0 Reorder the terms: -18 + 20x + 10x2 = 0 Solving -18 + 20x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 10x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 10x + 5x2)' equal to zero and attempt to solve: Simplifying -9 + 10x + 5x2 = 0 Solving -9 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 2x + x2 = 0 + 1.8 2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 2x + x2 = 1.8 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 = 1.8 + 1 Reorder the terms: 1 + 2x + x2 = 1.8 + 1 Combine like terms: 1.8 + 1 = 2.8 1 + 2x + x2 = 2.8 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.8 Calculate the square root of the right side: 1.673320053 Break this problem into two subproblems by setting (x + 1) equal to 1.673320053 and -1.673320053.Subproblem 1
x + 1 = 1.673320053 Simplifying x + 1 = 1.673320053 Reorder the terms: 1 + x = 1.673320053 Solving 1 + x = 1.673320053 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 = 1.673320053 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.673320053 + -1 x = 1.673320053 + -1 Combine like terms: 1.673320053 + -1 = 0.673320053 x = 0.673320053 Simplifying x = 0.673320053Subproblem 2
x + 1 = -1.673320053 Simplifying x + 1 = -1.673320053 Reorder the terms: 1 + x = -1.673320053 Solving 1 + x = -1.673320053 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 = -1.673320053 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.673320053 + -1 x = -1.673320053 + -1 Combine like terms: -1.673320053 + -1 = -2.673320053 x = -2.673320053 Simplifying x = -2.673320053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.673320053, -2.673320053}Solution
x = {0.673320053, -2.673320053}
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