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Simplifying 0.02x2 + -0.3x = 20 Reorder the terms: -0.3x + 0.02x2 = 20 Solving -0.3x + 0.02x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -0.3x + 0.02x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -0.3x + 0.02x2 = 0 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -1000 + -15x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -15x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -15x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -15x + x2 = 0 + 1000 -15x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -15x + x2 = 1000 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 1000 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 1000 + 56.25 Combine like terms: 1000 + 56.25 = 1056.25 56.25 + -15x + x2 = 1056.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 1056.25 Calculate the square root of the right side: 32.5 Break this problem into two subproblems by setting (x + -7.5) equal to 32.5 and -32.5.Subproblem 1
x + -7.5 = 32.5 Simplifying x + -7.5 = 32.5 Reorder the terms: -7.5 + x = 32.5 Solving -7.5 + x = 32.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 32.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 32.5 + 7.5 x = 32.5 + 7.5 Combine like terms: 32.5 + 7.5 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -7.5 = -32.5 Simplifying x + -7.5 = -32.5 Reorder the terms: -7.5 + x = -32.5 Solving -7.5 + x = -32.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -32.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -32.5 + 7.5 x = -32.5 + 7.5 Combine like terms: -32.5 + 7.5 = -25 x = -25 Simplifying x = -25Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -25}
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