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Simplifying -0.01x2 + 0.07x = -6.4 Reorder the terms: 0.07x + -0.01x2 = -6.4 Solving 0.07x + -0.01x2 = -6.4 Solving for variable 'x'. Reorder the terms: 6.4 + 0.07x + -0.01x2 = -6.4 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 6.4 + 0.07x + -0.01x2 = 0.0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -640 + -7x + x2 = 0 Move the constant term to the right: Add '640' to each side of the equation. -640 + -7x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + -7x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + -7x + x2 = 0 + 640 -7x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 -7x + x2 = 640 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 640 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 640 + 12.25 Combine like terms: 640 + 12.25 = 652.25 12.25 + -7x + x2 = 652.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 652.25 Calculate the square root of the right side: 25.539185578 Break this problem into two subproblems by setting (x + -3.5) equal to 25.539185578 and -25.539185578.Subproblem 1
x + -3.5 = 25.539185578 Simplifying x + -3.5 = 25.539185578 Reorder the terms: -3.5 + x = 25.539185578 Solving -3.5 + x = 25.539185578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 25.539185578 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 25.539185578 + 3.5 x = 25.539185578 + 3.5 Combine like terms: 25.539185578 + 3.5 = 29.039185578 x = 29.039185578 Simplifying x = 29.039185578Subproblem 2
x + -3.5 = -25.539185578 Simplifying x + -3.5 = -25.539185578 Reorder the terms: -3.5 + x = -25.539185578 Solving -3.5 + x = -25.539185578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -25.539185578 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -25.539185578 + 3.5 x = -25.539185578 + 3.5 Combine like terms: -25.539185578 + 3.5 = -22.039185578 x = -22.039185578 Simplifying x = -22.039185578Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.039185578, -22.039185578}
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