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Simplifying 5470 = 10x2 + 305x + 4000 Reorder the terms: 5470 = 4000 + 305x + 10x2 Solving 5470 = 4000 + 305x + 10x2 Solving for variable 'x'. Combine like terms: 5470 + -4000 = 1470 1470 + -305x + -10x2 = 4000 + 305x + 10x2 + -4000 + -305x + -10x2 Reorder the terms: 1470 + -305x + -10x2 = 4000 + -4000 + 305x + -305x + 10x2 + -10x2 Combine like terms: 4000 + -4000 = 0 1470 + -305x + -10x2 = 0 + 305x + -305x + 10x2 + -10x2 1470 + -305x + -10x2 = 305x + -305x + 10x2 + -10x2 Combine like terms: 305x + -305x = 0 1470 + -305x + -10x2 = 0 + 10x2 + -10x2 1470 + -305x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 1470 + -305x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(294 + -61x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(294 + -61x + -2x2)' equal to zero and attempt to solve: Simplifying 294 + -61x + -2x2 = 0 Solving 294 + -61x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -147 + 30.5x + x2 = 0 Move the constant term to the right: Add '147' to each side of the equation. -147 + 30.5x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 30.5x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 30.5x + x2 = 0 + 147 30.5x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 30.5x + x2 = 147 The x term is 30.5x. Take half its coefficient (15.25). Square it (232.5625) and add it to both sides. Add '232.5625' to each side of the equation. 30.5x + 232.5625 + x2 = 147 + 232.5625 Reorder the terms: 232.5625 + 30.5x + x2 = 147 + 232.5625 Combine like terms: 147 + 232.5625 = 379.5625 232.5625 + 30.5x + x2 = 379.5625 Factor a perfect square on the left side: (x + 15.25)(x + 15.25) = 379.5625 Calculate the square root of the right side: 19.48236382 Break this problem into two subproblems by setting (x + 15.25) equal to 19.48236382 and -19.48236382.Subproblem 1
x + 15.25 = 19.48236382 Simplifying x + 15.25 = 19.48236382 Reorder the terms: 15.25 + x = 19.48236382 Solving 15.25 + x = 19.48236382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.25' to each side of the equation. 15.25 + -15.25 + x = 19.48236382 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + x = 19.48236382 + -15.25 x = 19.48236382 + -15.25 Combine like terms: 19.48236382 + -15.25 = 4.23236382 x = 4.23236382 Simplifying x = 4.23236382Subproblem 2
x + 15.25 = -19.48236382 Simplifying x + 15.25 = -19.48236382 Reorder the terms: 15.25 + x = -19.48236382 Solving 15.25 + x = -19.48236382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.25' to each side of the equation. 15.25 + -15.25 + x = -19.48236382 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + x = -19.48236382 + -15.25 x = -19.48236382 + -15.25 Combine like terms: -19.48236382 + -15.25 = -34.73236382 x = -34.73236382 Simplifying x = -34.73236382Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.23236382, -34.73236382}Solution
x = {4.23236382, -34.73236382}
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