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Simplifying 3 = x(x + 3.75) Reorder the terms: 3 = x(3.75 + x) 3 = (3.75 * x + x * x) 3 = (3.75x + x2) Solving 3 = 3.75x + x2 Solving for variable 'x'. Reorder the terms: 3 + -3.75x + -1x2 = 3.75x + -3.75x + x2 + -1x2 Combine like terms: 3.75x + -3.75x = 0.00 3 + -3.75x + -1x2 = 0.00 + x2 + -1x2 3 + -3.75x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + -3.75x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 3.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.75x + x2 = 0 + 3 3.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.75x + x2 = 3 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 3 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 3 + 3.515625 Combine like terms: 3 + 3.515625 = 6.515625 3.515625 + 3.75x + x2 = 6.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 6.515625 Calculate the square root of the right side: 2.552572232 Break this problem into two subproblems by setting (x + 1.875) equal to 2.552572232 and -2.552572232.Subproblem 1
x + 1.875 = 2.552572232 Simplifying x + 1.875 = 2.552572232 Reorder the terms: 1.875 + x = 2.552572232 Solving 1.875 + x = 2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.552572232 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.552572232 + -1.875 x = 2.552572232 + -1.875 Combine like terms: 2.552572232 + -1.875 = 0.677572232 x = 0.677572232 Simplifying x = 0.677572232Subproblem 2
x + 1.875 = -2.552572232 Simplifying x + 1.875 = -2.552572232 Reorder the terms: 1.875 + x = -2.552572232 Solving 1.875 + x = -2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.552572232 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.552572232 + -1.875 x = -2.552572232 + -1.875 Combine like terms: -2.552572232 + -1.875 = -4.427572232 x = -4.427572232 Simplifying x = -4.427572232Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.677572232, -4.427572232}
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