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Simplifying 25x2 + 30x + 225 = 237 Reorder the terms: 225 + 30x + 25x2 = 237 Solving 225 + 30x + 25x2 = 237 Solving for variable 'x'. Reorder the terms: 225 + -237 + 30x + 25x2 = 237 + -237 Combine like terms: 225 + -237 = -12 -12 + 30x + 25x2 = 237 + -237 Combine like terms: 237 + -237 = 0 -12 + 30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + 1.2x + 0.48 + x2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + 1.2x + x2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + 1.2x + x2 = 0 + 0.48 1.2x + x2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 1.2x + x2 = 0.48 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 0.48 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.48 + 0.36 Combine like terms: 0.48 + 0.36 = 0.84 0.36 + 1.2x + x2 = 0.84 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + 0.6) equal to 0.916515139 and -0.916515139.Subproblem 1
x + 0.6 = 0.916515139 Simplifying x + 0.6 = 0.916515139 Reorder the terms: 0.6 + x = 0.916515139 Solving 0.6 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.916515139 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.916515139 + -0.6 x = 0.916515139 + -0.6 Combine like terms: 0.916515139 + -0.6 = 0.316515139 x = 0.316515139 Simplifying x = 0.316515139Subproblem 2
x + 0.6 = -0.916515139 Simplifying x + 0.6 = -0.916515139 Reorder the terms: 0.6 + x = -0.916515139 Solving 0.6 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.916515139 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.916515139 + -0.6 x = -0.916515139 + -0.6 Combine like terms: -0.916515139 + -0.6 = -1.516515139 x = -1.516515139 Simplifying x = -1.516515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.316515139, -1.516515139}
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