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Simplifying 4x2 + 130x = 833.33 Reorder the terms: 130x + 4x2 = 833.33 Solving 130x + 4x2 = 833.33 Solving for variable 'x'. Reorder the terms: -833.33 + 130x + 4x2 = 833.33 + -833.33 Combine like terms: 833.33 + -833.33 = 0.00 -833.33 + 130x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -208.3325 + 32.5x + x2 = 0.00 Move the constant term to the right: Add '208.3325' to each side of the equation. -208.3325 + 32.5x + 208.3325 + x2 = 0.00 + 208.3325 Reorder the terms: -208.3325 + 208.3325 + 32.5x + x2 = 0.00 + 208.3325 Combine like terms: -208.3325 + 208.3325 = 0.0000 0.0000 + 32.5x + x2 = 0.00 + 208.3325 32.5x + x2 = 0.00 + 208.3325 Combine like terms: 0.00 + 208.3325 = 208.3325 32.5x + x2 = 208.3325 The x term is 32.5x. Take half its coefficient (16.25). Square it (264.0625) and add it to both sides. Add '264.0625' to each side of the equation. 32.5x + 264.0625 + x2 = 208.3325 + 264.0625 Reorder the terms: 264.0625 + 32.5x + x2 = 208.3325 + 264.0625 Combine like terms: 208.3325 + 264.0625 = 472.395 264.0625 + 32.5x + x2 = 472.395 Factor a perfect square on the left side: (x + 16.25)(x + 16.25) = 472.395 Calculate the square root of the right side: 21.734649756 Break this problem into two subproblems by setting (x + 16.25) equal to 21.734649756 and -21.734649756.Subproblem 1
x + 16.25 = 21.734649756 Simplifying x + 16.25 = 21.734649756 Reorder the terms: 16.25 + x = 21.734649756 Solving 16.25 + x = 21.734649756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.25' to each side of the equation. 16.25 + -16.25 + x = 21.734649756 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = 21.734649756 + -16.25 x = 21.734649756 + -16.25 Combine like terms: 21.734649756 + -16.25 = 5.484649756 x = 5.484649756 Simplifying x = 5.484649756Subproblem 2
x + 16.25 = -21.734649756 Simplifying x + 16.25 = -21.734649756 Reorder the terms: 16.25 + x = -21.734649756 Solving 16.25 + x = -21.734649756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.25' to each side of the equation. 16.25 + -16.25 + x = -21.734649756 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = -21.734649756 + -16.25 x = -21.734649756 + -16.25 Combine like terms: -21.734649756 + -16.25 = -37.984649756 x = -37.984649756 Simplifying x = -37.984649756Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.484649756, -37.984649756}
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