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Simplifying -0.005x2 + 0.45x + -7 = 0 Reorder the terms: -7 + 0.45x + -0.005x2 = 0 Solving -7 + 0.45x + -0.005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. 1400 + -90x + x2 = 0 Move the constant term to the right: Add '-1400' to each side of the equation. 1400 + -90x + -1400 + x2 = 0 + -1400 Reorder the terms: 1400 + -1400 + -90x + x2 = 0 + -1400 Combine like terms: 1400 + -1400 = 0 0 + -90x + x2 = 0 + -1400 -90x + x2 = 0 + -1400 Combine like terms: 0 + -1400 = -1400 -90x + x2 = -1400 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -1400 + 2025 Reorder the terms: 2025 + -90x + x2 = -1400 + 2025 Combine like terms: -1400 + 2025 = 625 2025 + -90x + x2 = 625 Factor a perfect square on the left side: (x + -45)(x + -45) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -45) equal to 25 and -25.Subproblem 1
x + -45 = 25 Simplifying x + -45 = 25 Reorder the terms: -45 + x = 25 Solving -45 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 25 + 45 Combine like terms: -45 + 45 = 0 0 + x = 25 + 45 x = 25 + 45 Combine like terms: 25 + 45 = 70 x = 70 Simplifying x = 70Subproblem 2
x + -45 = -25 Simplifying x + -45 = -25 Reorder the terms: -45 + x = -25 Solving -45 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -25 + 45 Combine like terms: -45 + 45 = 0 0 + x = -25 + 45 x = -25 + 45 Combine like terms: -25 + 45 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {70, 20}
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