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Simplifying 1.25(x2) + -3.8x + -7.6 = 0 Reorder the terms: -7.6 + -3.8x + 1.25x2 = 0 Solving -7.6 + -3.8x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -6.08 + -3.04x + x2 = 0 Move the constant term to the right: Add '6.08' to each side of the equation. -6.08 + -3.04x + 6.08 + x2 = 0 + 6.08 Reorder the terms: -6.08 + 6.08 + -3.04x + x2 = 0 + 6.08 Combine like terms: -6.08 + 6.08 = 0.00 0.00 + -3.04x + x2 = 0 + 6.08 -3.04x + x2 = 0 + 6.08 Combine like terms: 0 + 6.08 = 6.08 -3.04x + x2 = 6.08 The x term is -3.04x. Take half its coefficient (-1.52). Square it (2.3104) and add it to both sides. Add '2.3104' to each side of the equation. -3.04x + 2.3104 + x2 = 6.08 + 2.3104 Reorder the terms: 2.3104 + -3.04x + x2 = 6.08 + 2.3104 Combine like terms: 6.08 + 2.3104 = 8.3904 2.3104 + -3.04x + x2 = 8.3904 Factor a perfect square on the left side: (x + -1.52)(x + -1.52) = 8.3904 Calculate the square root of the right side: 2.896618718 Break this problem into two subproblems by setting (x + -1.52) equal to 2.896618718 and -2.896618718.Subproblem 1
x + -1.52 = 2.896618718 Simplifying x + -1.52 = 2.896618718 Reorder the terms: -1.52 + x = 2.896618718 Solving -1.52 + x = 2.896618718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.52' to each side of the equation. -1.52 + 1.52 + x = 2.896618718 + 1.52 Combine like terms: -1.52 + 1.52 = 0.00 0.00 + x = 2.896618718 + 1.52 x = 2.896618718 + 1.52 Combine like terms: 2.896618718 + 1.52 = 4.416618718 x = 4.416618718 Simplifying x = 4.416618718Subproblem 2
x + -1.52 = -2.896618718 Simplifying x + -1.52 = -2.896618718 Reorder the terms: -1.52 + x = -2.896618718 Solving -1.52 + x = -2.896618718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.52' to each side of the equation. -1.52 + 1.52 + x = -2.896618718 + 1.52 Combine like terms: -1.52 + 1.52 = 0.00 0.00 + x = -2.896618718 + 1.52 x = -2.896618718 + 1.52 Combine like terms: -2.896618718 + 1.52 = -1.376618718 x = -1.376618718 Simplifying x = -1.376618718Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.416618718, -1.376618718}
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