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Simplifying 0 = -5x2 + 40x + 3 Reorder the terms: 0 = 3 + 40x + -5x2 Solving 0 = 3 + 40x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -40x + 5x2 = 3 + 40x + -5x2 + -3 + -40x + 5x2 Reorder the terms: -3 + -40x + 5x2 = 3 + -3 + 40x + -40x + -5x2 + 5x2 Combine like terms: 3 + -3 = 0 -3 + -40x + 5x2 = 0 + 40x + -40x + -5x2 + 5x2 -3 + -40x + 5x2 = 40x + -40x + -5x2 + 5x2 Combine like terms: 40x + -40x = 0 -3 + -40x + 5x2 = 0 + -5x2 + 5x2 -3 + -40x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -3 + -40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -8x + x2 = 0 + 0.6 -8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -8x + x2 = 0.6 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 0.6 + 16 Reorder the terms: 16 + -8x + x2 = 0.6 + 16 Combine like terms: 0.6 + 16 = 16.6 16 + -8x + x2 = 16.6 Factor a perfect square on the left side: (x + -4)(x + -4) = 16.6 Calculate the square root of the right side: 4.074309757 Break this problem into two subproblems by setting (x + -4) equal to 4.074309757 and -4.074309757.Subproblem 1
x + -4 = 4.074309757 Simplifying x + -4 = 4.074309757 Reorder the terms: -4 + x = 4.074309757 Solving -4 + x = 4.074309757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.074309757 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.074309757 + 4 x = 4.074309757 + 4 Combine like terms: 4.074309757 + 4 = 8.074309757 x = 8.074309757 Simplifying x = 8.074309757Subproblem 2
x + -4 = -4.074309757 Simplifying x + -4 = -4.074309757 Reorder the terms: -4 + x = -4.074309757 Solving -4 + x = -4.074309757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.074309757 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.074309757 + 4 x = -4.074309757 + 4 Combine like terms: -4.074309757 + 4 = -0.074309757 x = -0.074309757 Simplifying x = -0.074309757Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.074309757, -0.074309757}
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