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Simplifying 0 = 0.04x2 + -1.3x + -56 Reorder the terms: 0 = -56 + -1.3x + 0.04x2 Solving 0 = -56 + -1.3x + 0.04x2 Solving for variable 'x'. Combine like terms: 0 + 56 = 56 56 + 1.3x + -0.04x2 = -56 + -1.3x + 0.04x2 + 56 + 1.3x + -0.04x2 Reorder the terms: 56 + 1.3x + -0.04x2 = -56 + 56 + -1.3x + 1.3x + 0.04x2 + -0.04x2 Combine like terms: -56 + 56 = 0 56 + 1.3x + -0.04x2 = 0 + -1.3x + 1.3x + 0.04x2 + -0.04x2 56 + 1.3x + -0.04x2 = -1.3x + 1.3x + 0.04x2 + -0.04x2 Combine like terms: -1.3x + 1.3x = 0.0 56 + 1.3x + -0.04x2 = 0.0 + 0.04x2 + -0.04x2 56 + 1.3x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 56 + 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'. -1400 + -32.5x + x2 = 0 Move the constant term to the right: Add '1400' to each side of the equation. -1400 + -32.5x + 1400 + x2 = 0 + 1400 Reorder the terms: -1400 + 1400 + -32.5x + x2 = 0 + 1400 Combine like terms: -1400 + 1400 = 0 0 + -32.5x + x2 = 0 + 1400 -32.5x + x2 = 0 + 1400 Combine like terms: 0 + 1400 = 1400 -32.5x + x2 = 1400 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 = 1400 + 264.0625 Reorder the terms: 264.0625 + -32.5x + x2 = 1400 + 264.0625 Combine like terms: 1400 + 264.0625 = 1664.0625 264.0625 + -32.5x + x2 = 1664.0625 Factor a perfect square on the left side: (x + -16.25)(x + -16.25) = 1664.0625 Calculate the square root of the right side: 40.79292218 Break this problem into two subproblems by setting (x + -16.25) equal to 40.79292218 and -40.79292218.Subproblem 1
x + -16.25 = 40.79292218 Simplifying x + -16.25 = 40.79292218 Reorder the terms: -16.25 + x = 40.79292218 Solving -16.25 + x = 40.79292218 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 = 40.79292218 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = 40.79292218 + 16.25 x = 40.79292218 + 16.25 Combine like terms: 40.79292218 + 16.25 = 57.04292218 x = 57.04292218 Simplifying x = 57.04292218Subproblem 2
x + -16.25 = -40.79292218 Simplifying x + -16.25 = -40.79292218 Reorder the terms: -16.25 + x = -40.79292218 Solving -16.25 + x = -40.79292218 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 = -40.79292218 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = -40.79292218 + 16.25 x = -40.79292218 + 16.25 Combine like terms: -40.79292218 + 16.25 = -24.54292218 x = -24.54292218 Simplifying x = -24.54292218Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.04292218, -24.54292218}
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