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Simplifying 10x2 + 18x + -102 = 0 Reorder the terms: -102 + 18x + 10x2 = 0 Solving -102 + 18x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-51 + 9x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-51 + 9x + 5x2)' equal to zero and attempt to solve: Simplifying -51 + 9x + 5x2 = 0 Solving -51 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.2 + 1.8x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + 1.8x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + 1.8x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + 1.8x + x2 = 0 + 10.2 1.8x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 1.8x + x2 = 10.2 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 10.2 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 10.2 + 0.81 Combine like terms: 10.2 + 0.81 = 11.01 0.81 + 1.8x + x2 = 11.01 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 11.01 Calculate the square root of the right side: 3.318132005 Break this problem into two subproblems by setting (x + 0.9) equal to 3.318132005 and -3.318132005.Subproblem 1
x + 0.9 = 3.318132005 Simplifying x + 0.9 = 3.318132005 Reorder the terms: 0.9 + x = 3.318132005 Solving 0.9 + x = 3.318132005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 3.318132005 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 3.318132005 + -0.9 x = 3.318132005 + -0.9 Combine like terms: 3.318132005 + -0.9 = 2.418132005 x = 2.418132005 Simplifying x = 2.418132005Subproblem 2
x + 0.9 = -3.318132005 Simplifying x + 0.9 = -3.318132005 Reorder the terms: 0.9 + x = -3.318132005 Solving 0.9 + x = -3.318132005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -3.318132005 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -3.318132005 + -0.9 x = -3.318132005 + -0.9 Combine like terms: -3.318132005 + -0.9 = -4.218132005 x = -4.218132005 Simplifying x = -4.218132005Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.418132005, -4.218132005}Solution
x = {2.418132005, -4.218132005}
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