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Simplifying 4x2 + -210x + 2450 = 1000 Reorder the terms: 2450 + -210x + 4x2 = 1000 Solving 2450 + -210x + 4x2 = 1000 Solving for variable 'x'. Reorder the terms: 2450 + -1000 + -210x + 4x2 = 1000 + -1000 Combine like terms: 2450 + -1000 = 1450 1450 + -210x + 4x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 1450 + -210x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(725 + -105x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(725 + -105x + 2x2)' equal to zero and attempt to solve: Simplifying 725 + -105x + 2x2 = 0 Solving 725 + -105x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 362.5 + -52.5x + x2 = 0 Move the constant term to the right: Add '-362.5' to each side of the equation. 362.5 + -52.5x + -362.5 + x2 = 0 + -362.5 Reorder the terms: 362.5 + -362.5 + -52.5x + x2 = 0 + -362.5 Combine like terms: 362.5 + -362.5 = 0.0 0.0 + -52.5x + x2 = 0 + -362.5 -52.5x + x2 = 0 + -362.5 Combine like terms: 0 + -362.5 = -362.5 -52.5x + x2 = -362.5 The x term is -52.5x. Take half its coefficient (-26.25). Square it (689.0625) and add it to both sides. Add '689.0625' to each side of the equation. -52.5x + 689.0625 + x2 = -362.5 + 689.0625 Reorder the terms: 689.0625 + -52.5x + x2 = -362.5 + 689.0625 Combine like terms: -362.5 + 689.0625 = 326.5625 689.0625 + -52.5x + x2 = 326.5625 Factor a perfect square on the left side: (x + -26.25)(x + -26.25) = 326.5625 Calculate the square root of the right side: 18.071040369 Break this problem into two subproblems by setting (x + -26.25) equal to 18.071040369 and -18.071040369.Subproblem 1
x + -26.25 = 18.071040369 Simplifying x + -26.25 = 18.071040369 Reorder the terms: -26.25 + x = 18.071040369 Solving -26.25 + x = 18.071040369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.25' to each side of the equation. -26.25 + 26.25 + x = 18.071040369 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = 18.071040369 + 26.25 x = 18.071040369 + 26.25 Combine like terms: 18.071040369 + 26.25 = 44.321040369 x = 44.321040369 Simplifying x = 44.321040369Subproblem 2
x + -26.25 = -18.071040369 Simplifying x + -26.25 = -18.071040369 Reorder the terms: -26.25 + x = -18.071040369 Solving -26.25 + x = -18.071040369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.25' to each side of the equation. -26.25 + 26.25 + x = -18.071040369 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = -18.071040369 + 26.25 x = -18.071040369 + 26.25 Combine like terms: -18.071040369 + 26.25 = 8.178959631 x = 8.178959631 Simplifying x = 8.178959631Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.321040369, 8.178959631}Solution
x = {44.321040369, 8.178959631}
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