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Simplifying x2 + -1(441 + -84x + 4x2) = 21 x2 + (441 * -1 + -84x * -1 + 4x2 * -1) = 21 x2 + (-441 + 84x + -4x2) = 21 Reorder the terms: -441 + 84x + x2 + -4x2 = 21 Combine like terms: x2 + -4x2 = -3x2 -441 + 84x + -3x2 = 21 Solving -441 + 84x + -3x2 = 21 Solving for variable 'x'. Reorder the terms: -441 + -21 + 84x + -3x2 = 21 + -21 Combine like terms: -441 + -21 = -462 -462 + 84x + -3x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -462 + 84x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-154 + 28x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-154 + 28x + -1x2)' equal to zero and attempt to solve: Simplifying -154 + 28x + -1x2 = 0 Solving -154 + 28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 154 + -28x + x2 = 0 Move the constant term to the right: Add '-154' to each side of the equation. 154 + -28x + -154 + x2 = 0 + -154 Reorder the terms: 154 + -154 + -28x + x2 = 0 + -154 Combine like terms: 154 + -154 = 0 0 + -28x + x2 = 0 + -154 -28x + x2 = 0 + -154 Combine like terms: 0 + -154 = -154 -28x + x2 = -154 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -154 + 196 Reorder the terms: 196 + -28x + x2 = -154 + 196 Combine like terms: -154 + 196 = 42 196 + -28x + x2 = 42 Factor a perfect square on the left side: (x + -14)(x + -14) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + -14) equal to 6.480740698 and -6.480740698.Subproblem 1
x + -14 = 6.480740698 Simplifying x + -14 = 6.480740698 Reorder the terms: -14 + x = 6.480740698 Solving -14 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 6.480740698 + 14 Combine like terms: -14 + 14 = 0 0 + x = 6.480740698 + 14 x = 6.480740698 + 14 Combine like terms: 6.480740698 + 14 = 20.480740698 x = 20.480740698 Simplifying x = 20.480740698Subproblem 2
x + -14 = -6.480740698 Simplifying x + -14 = -6.480740698 Reorder the terms: -14 + x = -6.480740698 Solving -14 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -6.480740698 + 14 Combine like terms: -14 + 14 = 0 0 + x = -6.480740698 + 14 x = -6.480740698 + 14 Combine like terms: -6.480740698 + 14 = 7.519259302 x = 7.519259302 Simplifying x = 7.519259302Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.480740698, 7.519259302}Solution
x = {20.480740698, 7.519259302}
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