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Simplifying 2x * 2x + 1 * 1 + -3x = 5 Reorder the terms for easier multiplication: 2 * 2x * x + 1 * 1 + -3x = 5 Multiply 2 * 2 4x * x + 1 * 1 + -3x = 5 Multiply x * x 4x^{2}+ 1 * 1 + -3x = 5 Multiply 1 * 1 4x^{2}+ 1 + -3x = 5 Reorder the terms: 1 + -3x + 4x^{2}= 5 Solving 1 + -3x + 4x^{2}= 5 Solving for variable 'x'. Reorder the terms: 1 + -5 + -3x + 4x^{2}= 5 + -5 Combine like terms: 1 + -5 = -4 -4 + -3x + 4x^{2}= 5 + -5 Combine like terms: 5 + -5 = 0 -4 + -3x + 4x^{2}= 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -0.75x + x^{2}= 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.75x + 1 + x^{2}= 0 + 1 Reorder the terms: -1 + 1 + -0.75x + x^{2}= 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.75x + x^{2}= 0 + 1 -0.75x + x^{2}= 0 + 1 Combine like terms: 0 + 1 = 1 -0.75x + x^{2}= 1 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x^{2}= 1 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x^{2}= 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + -0.75x + x^{2}= 1.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + -0.375) equal to 1.068000468 and -1.068000468.## Subproblem 1

x + -0.375 = 1.068000468 Simplifying x + -0.375 = 1.068000468 Reorder the terms: -0.375 + x = 1.068000468 Solving -0.375 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.068000468 + 0.375 x = 1.068000468 + 0.375 Combine like terms: 1.068000468 + 0.375 = 1.443000468 x = 1.443000468 Simplifying x = 1.443000468## Subproblem 2

x + -0.375 = -1.068000468 Simplifying x + -0.375 = -1.068000468 Reorder the terms: -0.375 + x = -1.068000468 Solving -0.375 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.068000468 + 0.375 x = -1.068000468 + 0.375 Combine like terms: -1.068000468 + 0.375 = -0.693000468 x = -0.693000468 Simplifying x = -0.693000468## Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.443000468, -0.693000468}

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