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Simplifying -5x2 + 3.25x + 1.5 = 0 Reorder the terms: 1.5 + 3.25x + -5x2 = 0 Solving 1.5 + 3.25x + -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'. -0.3 + -0.65x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.65x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.65x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.65x + x2 = 0 + 0.3 -0.65x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -0.65x + x2 = 0.3 The x term is -0.65x. Take half its coefficient (-0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. -0.65x + 0.105625 + x2 = 0.3 + 0.105625 Reorder the terms: 0.105625 + -0.65x + x2 = 0.3 + 0.105625 Combine like terms: 0.3 + 0.105625 = 0.405625 0.105625 + -0.65x + x2 = 0.405625 Factor a perfect square on the left side: (x + -0.325)(x + -0.325) = 0.405625 Calculate the square root of the right side: 0.63688696 Break this problem into two subproblems by setting (x + -0.325) equal to 0.63688696 and -0.63688696.Subproblem 1
x + -0.325 = 0.63688696 Simplifying x + -0.325 = 0.63688696 Reorder the terms: -0.325 + x = 0.63688696 Solving -0.325 + x = 0.63688696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + x = 0.63688696 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + x = 0.63688696 + 0.325 x = 0.63688696 + 0.325 Combine like terms: 0.63688696 + 0.325 = 0.96188696 x = 0.96188696 Simplifying x = 0.96188696Subproblem 2
x + -0.325 = -0.63688696 Simplifying x + -0.325 = -0.63688696 Reorder the terms: -0.325 + x = -0.63688696 Solving -0.325 + x = -0.63688696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + x = -0.63688696 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + x = -0.63688696 + 0.325 x = -0.63688696 + 0.325 Combine like terms: -0.63688696 + 0.325 = -0.31188696 x = -0.31188696 Simplifying x = -0.31188696Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96188696, -0.31188696}
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