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Simplifying 3x + -3 + 2(2x) + 17 = -2 + -2x + (4x2 + -5) Remove parenthesis around (2x) 3x + -3 + 2 * 2x + 17 = -2 + -2x + (4x2 + -5) Multiply 2 * 2 3x + -3 + 4x + 17 = -2 + -2x + (4x2 + -5) Reorder the terms: -3 + 17 + 3x + 4x = -2 + -2x + (4x2 + -5) Combine like terms: -3 + 17 = 14 14 + 3x + 4x = -2 + -2x + (4x2 + -5) Combine like terms: 3x + 4x = 7x 14 + 7x = -2 + -2x + (4x2 + -5) Reorder the terms: 14 + 7x = -2 + -2x + (-5 + 4x2) Remove parenthesis around (-5 + 4x2) 14 + 7x = -2 + -2x + -5 + 4x2 Reorder the terms: 14 + 7x = -2 + -5 + -2x + 4x2 Combine like terms: -2 + -5 = -7 14 + 7x = -7 + -2x + 4x2 Solving 14 + 7x = -7 + -2x + 4x2 Solving for variable 'x'. Reorder the terms: 14 + 7 + 7x + 2x + -4x2 = -7 + -2x + 4x2 + 7 + 2x + -4x2 Combine like terms: 14 + 7 = 21 21 + 7x + 2x + -4x2 = -7 + -2x + 4x2 + 7 + 2x + -4x2 Combine like terms: 7x + 2x = 9x 21 + 9x + -4x2 = -7 + -2x + 4x2 + 7 + 2x + -4x2 Reorder the terms: 21 + 9x + -4x2 = -7 + 7 + -2x + 2x + 4x2 + -4x2 Combine like terms: -7 + 7 = 0 21 + 9x + -4x2 = 0 + -2x + 2x + 4x2 + -4x2 21 + 9x + -4x2 = -2x + 2x + 4x2 + -4x2 Combine like terms: -2x + 2x = 0 21 + 9x + -4x2 = 0 + 4x2 + -4x2 21 + 9x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 21 + 9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + -2.25x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -2.25x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -2.25x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -2.25x + x2 = 0 + 5.25 -2.25x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -2.25x + x2 = 5.25 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 5.25 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 5.25 + 1.265625 Combine like terms: 5.25 + 1.265625 = 6.515625 1.265625 + -2.25x + x2 = 6.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 6.515625 Calculate the square root of the right side: 2.552572232 Break this problem into two subproblems by setting (x + -1.125) equal to 2.552572232 and -2.552572232.Subproblem 1
x + -1.125 = 2.552572232 Simplifying x + -1.125 = 2.552572232 Reorder the terms: -1.125 + x = 2.552572232 Solving -1.125 + x = 2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.552572232 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.552572232 + 1.125 x = 2.552572232 + 1.125 Combine like terms: 2.552572232 + 1.125 = 3.677572232 x = 3.677572232 Simplifying x = 3.677572232Subproblem 2
x + -1.125 = -2.552572232 Simplifying x + -1.125 = -2.552572232 Reorder the terms: -1.125 + x = -2.552572232 Solving -1.125 + x = -2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.552572232 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.552572232 + 1.125 x = -2.552572232 + 1.125 Combine like terms: -2.552572232 + 1.125 = -1.427572232 x = -1.427572232 Simplifying x = -1.427572232Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.677572232, -1.427572232}
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