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Simplifying 0 = 4x2 + -4x + -10 Reorder the terms: 0 = -10 + -4x + 4x2 Solving 0 = -10 + -4x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + 4x + -4x2 = -10 + -4x + 4x2 + 10 + 4x + -4x2 Reorder the terms: 10 + 4x + -4x2 = -10 + 10 + -4x + 4x + 4x2 + -4x2 Combine like terms: -10 + 10 = 0 10 + 4x + -4x2 = 0 + -4x + 4x + 4x2 + -4x2 10 + 4x + -4x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 10 + 4x + -4x2 = 0 + 4x2 + -4x2 10 + 4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 10 + 4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 2x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2x + -2x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + -2x2 = 0 Solving 5 + 2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -1x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1x + x2 = 0 + 2.5 -1x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1x + x2 = 2.5 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 = 2.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + -1x + x2 = 2.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -0.5 = 1.658312395 Simplifying x + -0.5 = 1.658312395 Reorder the terms: -0.5 + x = 1.658312395 Solving -0.5 + x = 1.658312395 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 = 1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.658312395 + 0.5 x = 1.658312395 + 0.5 Combine like terms: 1.658312395 + 0.5 = 2.158312395 x = 2.158312395 Simplifying x = 2.158312395Subproblem 2
x + -0.5 = -1.658312395 Simplifying x + -0.5 = -1.658312395 Reorder the terms: -0.5 + x = -1.658312395 Solving -0.5 + x = -1.658312395 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 = -1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.658312395 + 0.5 x = -1.658312395 + 0.5 Combine like terms: -1.658312395 + 0.5 = -1.158312395 x = -1.158312395 Simplifying x = -1.158312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.158312395, -1.158312395}Solution
x = {2.158312395, -1.158312395}
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