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Simplifying 4x2 = 3x2 + 9x + 14 Reorder the terms: 4x2 = 14 + 9x + 3x2 Solving 4x2 = 14 + 9x + 3x2 Solving for variable 'x'. Reorder the terms: -14 + -9x + 4x2 + -3x2 = 14 + 9x + 3x2 + -14 + -9x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -14 + -9x + 1x2 = 14 + 9x + 3x2 + -14 + -9x + -3x2 Reorder the terms: -14 + -9x + 1x2 = 14 + -14 + 9x + -9x + 3x2 + -3x2 Combine like terms: 14 + -14 = 0 -14 + -9x + 1x2 = 0 + 9x + -9x + 3x2 + -3x2 -14 + -9x + 1x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 -14 + -9x + 1x2 = 0 + 3x2 + -3x2 -14 + -9x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -14 + -9x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -9x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -9x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -9x + x2 = 0 + 14 -9x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -9x + x2 = 14 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 14 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + -9x + x2 = 34.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -4.5 = 5.852349955 Simplifying x + -4.5 = 5.852349955 Reorder the terms: -4.5 + x = 5.852349955 Solving -4.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.852349955 + 4.5 x = 5.852349955 + 4.5 Combine like terms: 5.852349955 + 4.5 = 10.352349955 x = 10.352349955 Simplifying x = 10.352349955Subproblem 2
x + -4.5 = -5.852349955 Simplifying x + -4.5 = -5.852349955 Reorder the terms: -4.5 + x = -5.852349955 Solving -4.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.852349955 + 4.5 x = -5.852349955 + 4.5 Combine like terms: -5.852349955 + 4.5 = -1.352349955 x = -1.352349955 Simplifying x = -1.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.352349955, -1.352349955}
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