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Simplifying 250 = 1.3x + 0.04x2 Solving 250 = 1.3x + 0.04x2 Solving for variable 'x'. Reorder the terms: 250 + -1.3x + -0.04x2 = 1.3x + -1.3x + 0.04x2 + -0.04x2 Combine like terms: 1.3x + -1.3x = 0.0 250 + -1.3x + -0.04x2 = 0.0 + 0.04x2 + -0.04x2 250 + -1.3x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 250 + -1.3x + -0.04x2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -6250 + 32.5x + x2 = 0 Move the constant term to the right: Add '6250' to each side of the equation. -6250 + 32.5x + 6250 + x2 = 0 + 6250 Reorder the terms: -6250 + 6250 + 32.5x + x2 = 0 + 6250 Combine like terms: -6250 + 6250 = 0 0 + 32.5x + x2 = 0 + 6250 32.5x + x2 = 0 + 6250 Combine like terms: 0 + 6250 = 6250 32.5x + x2 = 6250 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 = 6250 + 264.0625 Reorder the terms: 264.0625 + 32.5x + x2 = 6250 + 264.0625 Combine like terms: 6250 + 264.0625 = 6514.0625 264.0625 + 32.5x + x2 = 6514.0625 Factor a perfect square on the left side: (x + 16.25)(x + 16.25) = 6514.0625 Calculate the square root of the right side: 80.709742287 Break this problem into two subproblems by setting (x + 16.25) equal to 80.709742287 and -80.709742287.Subproblem 1
x + 16.25 = 80.709742287 Simplifying x + 16.25 = 80.709742287 Reorder the terms: 16.25 + x = 80.709742287 Solving 16.25 + x = 80.709742287 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 = 80.709742287 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = 80.709742287 + -16.25 x = 80.709742287 + -16.25 Combine like terms: 80.709742287 + -16.25 = 64.459742287 x = 64.459742287 Simplifying x = 64.459742287Subproblem 2
x + 16.25 = -80.709742287 Simplifying x + 16.25 = -80.709742287 Reorder the terms: 16.25 + x = -80.709742287 Solving 16.25 + x = -80.709742287 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 = -80.709742287 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = -80.709742287 + -16.25 x = -80.709742287 + -16.25 Combine like terms: -80.709742287 + -16.25 = -96.959742287 x = -96.959742287 Simplifying x = -96.959742287Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.459742287, -96.959742287}
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