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Simplifying 50x2 + -4x + -40 = 0 Reorder the terms: -40 + -4x + 50x2 = 0 Solving -40 + -4x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -2x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -2x + 25x2)' equal to zero and attempt to solve: Simplifying -20 + -2x + 25x2 = 0 Solving -20 + -2x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.8 + -0.08x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.08x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.08x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.08x + x2 = 0 + 0.8 -0.08x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.08x + x2 = 0.8 The x term is -0.08x. Take half its coefficient (-0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. -0.08x + 0.0016 + x2 = 0.8 + 0.0016 Reorder the terms: 0.0016 + -0.08x + x2 = 0.8 + 0.0016 Combine like terms: 0.8 + 0.0016 = 0.8016 0.0016 + -0.08x + x2 = 0.8016 Factor a perfect square on the left side: (x + -0.04)(x + -0.04) = 0.8016 Calculate the square root of the right side: 0.895321171 Break this problem into two subproblems by setting (x + -0.04) equal to 0.895321171 and -0.895321171.Subproblem 1
x + -0.04 = 0.895321171 Simplifying x + -0.04 = 0.895321171 Reorder the terms: -0.04 + x = 0.895321171 Solving -0.04 + x = 0.895321171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + x = 0.895321171 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + x = 0.895321171 + 0.04 x = 0.895321171 + 0.04 Combine like terms: 0.895321171 + 0.04 = 0.935321171 x = 0.935321171 Simplifying x = 0.935321171Subproblem 2
x + -0.04 = -0.895321171 Simplifying x + -0.04 = -0.895321171 Reorder the terms: -0.04 + x = -0.895321171 Solving -0.04 + x = -0.895321171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + x = -0.895321171 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + x = -0.895321171 + 0.04 x = -0.895321171 + 0.04 Combine like terms: -0.895321171 + 0.04 = -0.855321171 x = -0.855321171 Simplifying x = -0.855321171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.935321171, -0.855321171}Solution
x = {0.935321171, -0.855321171}
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