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Simplifying 10x2 + -8x + -10 = 0 Reorder the terms: -10 + -8x + 10x2 = 0 Solving -10 + -8x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -4x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + -4x + 5x2 = 0 Solving -5 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.8x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8x + x2 = 0 + 1 -0.8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8x + x2 = 1 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 1 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1 + 0.16 Combine like terms: 1 + 0.16 = 1.16 0.16 + -0.8x + x2 = 1.16 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + -0.4) equal to 1.077032961 and -1.077032961.Subproblem 1
x + -0.4 = 1.077032961 Simplifying x + -0.4 = 1.077032961 Reorder the terms: -0.4 + x = 1.077032961 Solving -0.4 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.077032961 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.077032961 + 0.4 x = 1.077032961 + 0.4 Combine like terms: 1.077032961 + 0.4 = 1.477032961 x = 1.477032961 Simplifying x = 1.477032961Subproblem 2
x + -0.4 = -1.077032961 Simplifying x + -0.4 = -1.077032961 Reorder the terms: -0.4 + x = -1.077032961 Solving -0.4 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.077032961 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.077032961 + 0.4 x = -1.077032961 + 0.4 Combine like terms: -1.077032961 + 0.4 = -0.677032961 x = -0.677032961 Simplifying x = -0.677032961Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.477032961, -0.677032961}Solution
x = {1.477032961, -0.677032961}
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