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Simplifying 4x2 = 7x + 7.5 Reorder the terms: 4x2 = 7.5 + 7x Solving 4x2 = 7.5 + 7x Solving for variable 'x'. Reorder the terms: -7.5 + -7x + 4x2 = 7.5 + 7x + -7.5 + -7x Reorder the terms: -7.5 + -7x + 4x2 = 7.5 + -7.5 + 7x + -7x Combine like terms: 7.5 + -7.5 = 0.0 -7.5 + -7x + 4x2 = 0.0 + 7x + -7x -7.5 + -7x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -7.5 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.875 + -1.75x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -1.75x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -1.75x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -1.75x + x2 = 0 + 1.875 -1.75x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -1.75x + x2 = 1.875 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 = 1.875 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 1.875 + 0.765625 Combine like terms: 1.875 + 0.765625 = 2.640625 0.765625 + -1.75x + x2 = 2.640625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 2.640625 Calculate the square root of the right side: 1.625 Break this problem into two subproblems by setting (x + -0.875) equal to 1.625 and -1.625.Subproblem 1
x + -0.875 = 1.625 Simplifying x + -0.875 = 1.625 Reorder the terms: -0.875 + x = 1.625 Solving -0.875 + x = 1.625 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 = 1.625 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.625 + 0.875 x = 1.625 + 0.875 Combine like terms: 1.625 + 0.875 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -0.875 = -1.625 Simplifying x + -0.875 = -1.625 Reorder the terms: -0.875 + x = -1.625 Solving -0.875 + x = -1.625 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 = -1.625 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.625 + 0.875 x = -1.625 + 0.875 Combine like terms: -1.625 + 0.875 = -0.75 x = -0.75 Simplifying x = -0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -0.75}
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