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Simplifying 50 = 1.3x + 0.04x2 Solving 50 = 1.3x + 0.04x2 Solving for variable 'x'. Reorder the terms: 50 + -1.3x + -0.04x2 = 1.3x + -1.3x + 0.04x2 + -0.04x2 Combine like terms: 1.3x + -1.3x = 0.0 50 + -1.3x + -0.04x2 = 0.0 + 0.04x2 + -0.04x2 50 + -1.3x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 50 + -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'. -1250 + 32.5x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + 32.5x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + 32.5x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + 32.5x + x2 = 0 + 1250 32.5x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 32.5x + x2 = 1250 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 = 1250 + 264.0625 Reorder the terms: 264.0625 + 32.5x + x2 = 1250 + 264.0625 Combine like terms: 1250 + 264.0625 = 1514.0625 264.0625 + 32.5x + x2 = 1514.0625 Factor a perfect square on the left side: (x + 16.25)(x + 16.25) = 1514.0625 Calculate the square root of the right side: 38.910956041 Break this problem into two subproblems by setting (x + 16.25) equal to 38.910956041 and -38.910956041.Subproblem 1
x + 16.25 = 38.910956041 Simplifying x + 16.25 = 38.910956041 Reorder the terms: 16.25 + x = 38.910956041 Solving 16.25 + x = 38.910956041 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 = 38.910956041 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = 38.910956041 + -16.25 x = 38.910956041 + -16.25 Combine like terms: 38.910956041 + -16.25 = 22.660956041 x = 22.660956041 Simplifying x = 22.660956041Subproblem 2
x + 16.25 = -38.910956041 Simplifying x + 16.25 = -38.910956041 Reorder the terms: 16.25 + x = -38.910956041 Solving 16.25 + x = -38.910956041 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 = -38.910956041 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + x = -38.910956041 + -16.25 x = -38.910956041 + -16.25 Combine like terms: -38.910956041 + -16.25 = -55.160956041 x = -55.160956041 Simplifying x = -55.160956041Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.660956041, -55.160956041}
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