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Simplifying 5x2 + 3.25x = 1.5 Reorder the terms: 3.25x + 5x2 = 1.5 Solving 3.25x + 5x2 = 1.5 Solving for variable 'x'. Reorder the terms: -1.5 + 3.25x + 5x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + 3.25x + 5x2 = 0.0 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 = 0.0 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 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.65x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.65x + x2 = 0.0 + 0.3 0.65x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 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 = 0.31188696 x = 0.31188696 Simplifying x = 0.31188696Subproblem 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 = -0.96188696 x = -0.96188696 Simplifying x = -0.96188696Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31188696, -0.96188696}
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