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Simplifying 4x2 + 7x + -4.5 = 0 Reorder the terms: -4.5 + 7x + 4x2 = 0 Solving -4.5 + 7x + 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'. -1.125 + 1.75x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 1.75x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 1.75x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 1.75x + x2 = 0 + 1.125 1.75x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 1.75x + x2 = 1.125 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 1.125 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 1.125 + 0.765625 Combine like terms: 1.125 + 0.765625 = 1.890625 0.765625 + 1.75x + x2 = 1.890625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.890625 Calculate the square root of the right side: 1.375 Break this problem into two subproblems by setting (x + 0.875) equal to 1.375 and -1.375.Subproblem 1
x + 0.875 = 1.375 Simplifying x + 0.875 = 1.375 Reorder the terms: 0.875 + x = 1.375 Solving 0.875 + x = 1.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.375 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.375 + -0.875 x = 1.375 + -0.875 Combine like terms: 1.375 + -0.875 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 0.875 = -1.375 Simplifying x + 0.875 = -1.375 Reorder the terms: 0.875 + x = -1.375 Solving 0.875 + x = -1.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.375 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.375 + -0.875 x = -1.375 + -0.875 Combine like terms: -1.375 + -0.875 = -2.25 x = -2.25 Simplifying x = -2.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -2.25}
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