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Simplifying 4x2 + 4.5x + -2.25 = 0 Reorder the terms: -2.25 + 4.5x + 4x2 = 0 Solving -2.25 + 4.5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5625 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 1.125x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 1.125x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 1.125x + x2 = 0 + 0.5625 1.125x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 1.125x + x2 = 0.5625 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 0.5625 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.5625 + 0.31640625 Combine like terms: 0.5625 + 0.31640625 = 0.87890625 0.31640625 + 1.125x + x2 = 0.87890625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.87890625 Calculate the square root of the right side: 0.9375 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.9375 and -0.9375.Subproblem 1
x + 0.5625 = 0.9375 Simplifying x + 0.5625 = 0.9375 Reorder the terms: 0.5625 + x = 0.9375 Solving 0.5625 + x = 0.9375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.9375 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.9375 + -0.5625 x = 0.9375 + -0.5625 Combine like terms: 0.9375 + -0.5625 = 0.375 x = 0.375 Simplifying x = 0.375Subproblem 2
x + 0.5625 = -0.9375 Simplifying x + 0.5625 = -0.9375 Reorder the terms: 0.5625 + x = -0.9375 Solving 0.5625 + x = -0.9375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.9375 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.9375 + -0.5625 x = -0.9375 + -0.5625 Combine like terms: -0.9375 + -0.5625 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.375, -1.5}
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