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Simplifying 4x2 + 3x + 4 = 64 Reorder the terms: 4 + 3x + 4x2 = 64 Solving 4 + 3x + 4x2 = 64 Solving for variable 'x'. Reorder the terms: 4 + -64 + 3x + 4x2 = 64 + -64 Combine like terms: 4 + -64 = -60 -60 + 3x + 4x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -60 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + 0.75x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 0.75x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 0.75x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 0.75x + x2 = 0 + 15 0.75x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 0.75x + x2 = 15 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 + x2 = 15 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 15 + 0.140625 Combine like terms: 15 + 0.140625 = 15.140625 0.140625 + 0.75x + x2 = 15.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (x + 0.375) equal to 3.891095604 and -3.891095604.Subproblem 1
x + 0.375 = 3.891095604 Simplifying x + 0.375 = 3.891095604 Reorder the terms: 0.375 + x = 3.891095604 Solving 0.375 + x = 3.891095604 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 = 3.891095604 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.891095604 + -0.375 x = 3.891095604 + -0.375 Combine like terms: 3.891095604 + -0.375 = 3.516095604 x = 3.516095604 Simplifying x = 3.516095604Subproblem 2
x + 0.375 = -3.891095604 Simplifying x + 0.375 = -3.891095604 Reorder the terms: 0.375 + x = -3.891095604 Solving 0.375 + x = -3.891095604 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 = -3.891095604 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.891095604 + -0.375 x = -3.891095604 + -0.375 Combine like terms: -3.891095604 + -0.375 = -4.266095604 x = -4.266095604 Simplifying x = -4.266095604Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.516095604, -4.266095604}
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