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Simplifying 10x2 + -10x + -8 = 0 Reorder the terms: -8 + -10x + 10x2 = 0 Solving -8 + -10x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -5x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5x + 5x2)' equal to zero and attempt to solve: Simplifying -4 + -5x + 5x2 = 0 Solving -4 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -1x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1x + x2 = 0 + 0.8 -1x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1x + x2 = 0.8 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.8 + 0.25 Combine like terms: 0.8 + 0.25 = 1.05 0.25 + -1x + x2 = 1.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.05 Calculate the square root of the right side: 1.024695077 Break this problem into two subproblems by setting (x + -0.5) equal to 1.024695077 and -1.024695077.Subproblem 1
x + -0.5 = 1.024695077 Simplifying x + -0.5 = 1.024695077 Reorder the terms: -0.5 + x = 1.024695077 Solving -0.5 + x = 1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.024695077 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.024695077 + 0.5 x = 1.024695077 + 0.5 Combine like terms: 1.024695077 + 0.5 = 1.524695077 x = 1.524695077 Simplifying x = 1.524695077Subproblem 2
x + -0.5 = -1.024695077 Simplifying x + -0.5 = -1.024695077 Reorder the terms: -0.5 + x = -1.024695077 Solving -0.5 + x = -1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.024695077 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.024695077 + 0.5 x = -1.024695077 + 0.5 Combine like terms: -1.024695077 + 0.5 = -0.524695077 x = -0.524695077 Simplifying x = -0.524695077Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.524695077, -0.524695077}Solution
x = {1.524695077, -0.524695077}
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