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Simplifying 7x2 + -5x = 3x2 + 3 Reorder the terms: -5x + 7x2 = 3x2 + 3 Reorder the terms: -5x + 7x2 = 3 + 3x2 Solving -5x + 7x2 = 3 + 3x2 Solving for variable 'x'. Reorder the terms: -3 + -5x + 7x2 + -3x2 = 3 + 3x2 + -3 + -3x2 Combine like terms: 7x2 + -3x2 = 4x2 -3 + -5x + 4x2 = 3 + 3x2 + -3 + -3x2 Reorder the terms: -3 + -5x + 4x2 = 3 + -3 + 3x2 + -3x2 Combine like terms: 3 + -3 = 0 -3 + -5x + 4x2 = 0 + 3x2 + -3x2 -3 + -5x + 4x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -3 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.25x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.25x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.25x + x2 = 0 + 0.75 -1.25x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.25x + x2 = 0.75 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 0.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + -1.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + -0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
x + -0.625 = 1.068000468 Simplifying x + -0.625 = 1.068000468 Reorder the terms: -0.625 + x = 1.068000468 Solving -0.625 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.068000468 + 0.625 x = 1.068000468 + 0.625 Combine like terms: 1.068000468 + 0.625 = 1.693000468 x = 1.693000468 Simplifying x = 1.693000468Subproblem 2
x + -0.625 = -1.068000468 Simplifying x + -0.625 = -1.068000468 Reorder the terms: -0.625 + x = -1.068000468 Solving -0.625 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.068000468 + 0.625 x = -1.068000468 + 0.625 Combine like terms: -1.068000468 + 0.625 = -0.443000468 x = -0.443000468 Simplifying x = -0.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.693000468, -0.443000468}
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