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Simplifying 5x2 + -40x + 3 = 0 Reorder the terms: 3 + -40x + 5x2 = 0 Solving 3 + -40x + 5x2 = 0 Solving for variable 'x'. 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 = 15.4 16 + -8x + x2 = 15.4 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.4 Calculate the square root of the right side: 3.924283374 Break this problem into two subproblems by setting (x + -4) equal to 3.924283374 and -3.924283374.Subproblem 1
x + -4 = 3.924283374 Simplifying x + -4 = 3.924283374 Reorder the terms: -4 + x = 3.924283374 Solving -4 + x = 3.924283374 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 = 3.924283374 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.924283374 + 4 x = 3.924283374 + 4 Combine like terms: 3.924283374 + 4 = 7.924283374 x = 7.924283374 Simplifying x = 7.924283374Subproblem 2
x + -4 = -3.924283374 Simplifying x + -4 = -3.924283374 Reorder the terms: -4 + x = -3.924283374 Solving -4 + x = -3.924283374 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 = -3.924283374 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.924283374 + 4 x = -3.924283374 + 4 Combine like terms: -3.924283374 + 4 = 0.075716626 x = 0.075716626 Simplifying x = 0.075716626Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.924283374, 0.075716626}
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