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Simplifying 3 = 4x2 + 22x + 10 Reorder the terms: 3 = 10 + 22x + 4x2 Solving 3 = 10 + 22x + 4x2 Solving for variable 'x'. Combine like terms: 3 + -10 = -7 -7 + -22x + -4x2 = 10 + 22x + 4x2 + -10 + -22x + -4x2 Reorder the terms: -7 + -22x + -4x2 = 10 + -10 + 22x + -22x + 4x2 + -4x2 Combine like terms: 10 + -10 = 0 -7 + -22x + -4x2 = 0 + 22x + -22x + 4x2 + -4x2 -7 + -22x + -4x2 = 22x + -22x + 4x2 + -4x2 Combine like terms: 22x + -22x = 0 -7 + -22x + -4x2 = 0 + 4x2 + -4x2 -7 + -22x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -7 + -22x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 22x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 22x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 22x + 4x2 = 0 Solving 7 + 22x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 5.5x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 5.5x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 5.5x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 5.5x + x2 = 0 + -1.75 5.5x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 5.5x + x2 = -1.75 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -1.75 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -1.75 + 7.5625 Combine like terms: -1.75 + 7.5625 = 5.8125 7.5625 + 5.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + 2.75) equal to 2.41091269 and -2.41091269.Subproblem 1
x + 2.75 = 2.41091269 Simplifying x + 2.75 = 2.41091269 Reorder the terms: 2.75 + x = 2.41091269 Solving 2.75 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.41091269 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.41091269 + -2.75 x = 2.41091269 + -2.75 Combine like terms: 2.41091269 + -2.75 = -0.33908731 x = -0.33908731 Simplifying x = -0.33908731Subproblem 2
x + 2.75 = -2.41091269 Simplifying x + 2.75 = -2.41091269 Reorder the terms: 2.75 + x = -2.41091269 Solving 2.75 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.41091269 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.41091269 + -2.75 x = -2.41091269 + -2.75 Combine like terms: -2.41091269 + -2.75 = -5.16091269 x = -5.16091269 Simplifying x = -5.16091269Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.33908731, -5.16091269}Solution
x = {-0.33908731, -5.16091269}
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