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Simplifying (0.5)(-32x2) + 40x + 100 = 0 Remove parenthesis around (-32x2) 0.5 * -32x2 + 40x + 100 = 0 Multiply 0.5 * -32 -16x2 + 40x + 100 = 0 Reorder the terms: 100 + 40x + -16x2 = 0 Solving 100 + 40x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 10x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 10x + -4x2)' equal to zero and attempt to solve: Simplifying 25 + 10x + -4x2 = 0 Solving 25 + 10x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.5x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.5x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.5x + x2 = 0 + 6.25 -2.5x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.5x + x2 = 6.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 6.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6.25 + 1.5625 Combine like terms: 6.25 + 1.5625 = 7.8125 1.5625 + -2.5x + x2 = 7.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 7.8125 Calculate the square root of the right side: 2.795084972 Break this problem into two subproblems by setting (x + -1.25) equal to 2.795084972 and -2.795084972.Subproblem 1
x + -1.25 = 2.795084972 Simplifying x + -1.25 = 2.795084972 Reorder the terms: -1.25 + x = 2.795084972 Solving -1.25 + x = 2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.795084972 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.795084972 + 1.25 x = 2.795084972 + 1.25 Combine like terms: 2.795084972 + 1.25 = 4.045084972 x = 4.045084972 Simplifying x = 4.045084972Subproblem 2
x + -1.25 = -2.795084972 Simplifying x + -1.25 = -2.795084972 Reorder the terms: -1.25 + x = -2.795084972 Solving -1.25 + x = -2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.795084972 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.795084972 + 1.25 x = -2.795084972 + 1.25 Combine like terms: -2.795084972 + 1.25 = -1.545084972 x = -1.545084972 Simplifying x = -1.545084972Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.045084972, -1.545084972}Solution
x = {4.045084972, -1.545084972}
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