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Simplifying 0 = -0.04x2 + 0.8x + 3 Reorder the terms: 0 = 3 + 0.8x + -0.04x2 Solving 0 = 3 + 0.8x + -0.04x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -0.8x + 0.04x2 = 3 + 0.8x + -0.04x2 + -3 + -0.8x + 0.04x2 Reorder the terms: -3 + -0.8x + 0.04x2 = 3 + -3 + 0.8x + -0.8x + -0.04x2 + 0.04x2 Combine like terms: 3 + -3 = 0 -3 + -0.8x + 0.04x2 = 0 + 0.8x + -0.8x + -0.04x2 + 0.04x2 -3 + -0.8x + 0.04x2 = 0.8x + -0.8x + -0.04x2 + 0.04x2 Combine like terms: 0.8x + -0.8x = 0.0 -3 + -0.8x + 0.04x2 = 0.0 + -0.04x2 + 0.04x2 -3 + -0.8x + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 -3 + -0.8x + 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'. -75 + -20x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -20x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -20x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -20x + x2 = 0 + 75 -20x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -20x + x2 = 75 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 75 + 100 Reorder the terms: 100 + -20x + x2 = 75 + 100 Combine like terms: 75 + 100 = 175 100 + -20x + x2 = 175 Factor a perfect square on the left side: (x + -10)(x + -10) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -10) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -10 = 13.228756555 Simplifying x + -10 = 13.228756555 Reorder the terms: -10 + x = 13.228756555 Solving -10 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 13.228756555 + 10 Combine like terms: -10 + 10 = 0 0 + x = 13.228756555 + 10 x = 13.228756555 + 10 Combine like terms: 13.228756555 + 10 = 23.228756555 x = 23.228756555 Simplifying x = 23.228756555Subproblem 2
x + -10 = -13.228756555 Simplifying x + -10 = -13.228756555 Reorder the terms: -10 + x = -13.228756555 Solving -10 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -13.228756555 + 10 Combine like terms: -10 + 10 = 0 0 + x = -13.228756555 + 10 x = -13.228756555 + 10 Combine like terms: -13.228756555 + 10 = -3.228756555 x = -3.228756555 Simplifying x = -3.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.228756555, -3.228756555}
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