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Simplifying 3x2 + -0.75x = 0.5 Reorder the terms: -0.75x + 3x2 = 0.5 Solving -0.75x + 3x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + -0.75x + 3x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + -0.75x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.1666666667 + -0.25x + x2 = 0.0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.25x + 0.1666666667 + x2 = 0.0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.25x + x2 = 0.0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0.0 + 0.1666666667 -0.25x + x2 = 0.0 + 0.1666666667 Combine like terms: 0.0 + 0.1666666667 = 0.1666666667 -0.25x + x2 = 0.1666666667 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.1666666667 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.1666666667 + 0.015625 Combine like terms: 0.1666666667 + 0.015625 = 0.1822916667 0.015625 + -0.25x + x2 = 0.1822916667 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.1822916667 Calculate the square root of the right side: 0.426956282 Break this problem into two subproblems by setting (x + -0.125) equal to 0.426956282 and -0.426956282.Subproblem 1
x + -0.125 = 0.426956282 Simplifying x + -0.125 = 0.426956282 Reorder the terms: -0.125 + x = 0.426956282 Solving -0.125 + x = 0.426956282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.426956282 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.426956282 + 0.125 x = 0.426956282 + 0.125 Combine like terms: 0.426956282 + 0.125 = 0.551956282 x = 0.551956282 Simplifying x = 0.551956282Subproblem 2
x + -0.125 = -0.426956282 Simplifying x + -0.125 = -0.426956282 Reorder the terms: -0.125 + x = -0.426956282 Solving -0.125 + x = -0.426956282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.426956282 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.426956282 + 0.125 x = -0.426956282 + 0.125 Combine like terms: -0.426956282 + 0.125 = -0.301956282 x = -0.301956282 Simplifying x = -0.301956282Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.551956282, -0.301956282}
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