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Simplifying 4400 = -10x2 + 256x + 3500 Reorder the terms: 4400 = 3500 + 256x + -10x2 Solving 4400 = 3500 + 256x + -10x2 Solving for variable 'x'. Combine like terms: 4400 + -3500 = 900 900 + -256x + 10x2 = 3500 + 256x + -10x2 + -3500 + -256x + 10x2 Reorder the terms: 900 + -256x + 10x2 = 3500 + -3500 + 256x + -256x + -10x2 + 10x2 Combine like terms: 3500 + -3500 = 0 900 + -256x + 10x2 = 0 + 256x + -256x + -10x2 + 10x2 900 + -256x + 10x2 = 256x + -256x + -10x2 + 10x2 Combine like terms: 256x + -256x = 0 900 + -256x + 10x2 = 0 + -10x2 + 10x2 900 + -256x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 900 + -256x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(450 + -128x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(450 + -128x + 5x2)' equal to zero and attempt to solve: Simplifying 450 + -128x + 5x2 = 0 Solving 450 + -128x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 90 + -25.6x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -25.6x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -25.6x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -25.6x + x2 = 0 + -90 -25.6x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -25.6x + x2 = -90 The x term is -25.6x. Take half its coefficient (-12.8). Square it (163.84) and add it to both sides. Add '163.84' to each side of the equation. -25.6x + 163.84 + x2 = -90 + 163.84 Reorder the terms: 163.84 + -25.6x + x2 = -90 + 163.84 Combine like terms: -90 + 163.84 = 73.84 163.84 + -25.6x + x2 = 73.84 Factor a perfect square on the left side: (x + -12.8)(x + -12.8) = 73.84 Calculate the square root of the right side: 8.593020424 Break this problem into two subproblems by setting (x + -12.8) equal to 8.593020424 and -8.593020424.Subproblem 1
x + -12.8 = 8.593020424 Simplifying x + -12.8 = 8.593020424 Reorder the terms: -12.8 + x = 8.593020424 Solving -12.8 + x = 8.593020424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.8' to each side of the equation. -12.8 + 12.8 + x = 8.593020424 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + x = 8.593020424 + 12.8 x = 8.593020424 + 12.8 Combine like terms: 8.593020424 + 12.8 = 21.393020424 x = 21.393020424 Simplifying x = 21.393020424Subproblem 2
x + -12.8 = -8.593020424 Simplifying x + -12.8 = -8.593020424 Reorder the terms: -12.8 + x = -8.593020424 Solving -12.8 + x = -8.593020424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.8' to each side of the equation. -12.8 + 12.8 + x = -8.593020424 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + x = -8.593020424 + 12.8 x = -8.593020424 + 12.8 Combine like terms: -8.593020424 + 12.8 = 4.206979576 x = 4.206979576 Simplifying x = 4.206979576Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.393020424, 4.206979576}Solution
x = {21.393020424, 4.206979576}
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