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Simplifying -4.9x2 + 14x + 25 = 0 Reorder the terms: 25 + 14x + -4.9x2 = 0 Solving 25 + 14x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -5.102040816 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '5.102040816' to each side of the equation. -5.102040816 + -2.857142857x + 5.102040816 + x2 = 0 + 5.102040816 Reorder the terms: -5.102040816 + 5.102040816 + -2.857142857x + x2 = 0 + 5.102040816 Combine like terms: -5.102040816 + 5.102040816 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + 5.102040816 -2.857142857x + x2 = 0 + 5.102040816 Combine like terms: 0 + 5.102040816 = 5.102040816 -2.857142857x + x2 = 5.102040816 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 5.102040816 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 5.102040816 + 2.040816328 Combine like terms: 5.102040816 + 2.040816328 = 7.142857144 2.040816328 + -2.857142857x + x2 = 7.142857144 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 7.142857144 Calculate the square root of the right side: 2.672612419 Break this problem into two subproblems by setting (x + -1.428571429) equal to 2.672612419 and -2.672612419.Subproblem 1
x + -1.428571429 = 2.672612419 Simplifying x + -1.428571429 = 2.672612419 Reorder the terms: -1.428571429 + x = 2.672612419 Solving -1.428571429 + x = 2.672612419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 2.672612419 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 2.672612419 + 1.428571429 x = 2.672612419 + 1.428571429 Combine like terms: 2.672612419 + 1.428571429 = 4.101183848 x = 4.101183848 Simplifying x = 4.101183848Subproblem 2
x + -1.428571429 = -2.672612419 Simplifying x + -1.428571429 = -2.672612419 Reorder the terms: -1.428571429 + x = -2.672612419 Solving -1.428571429 + x = -2.672612419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -2.672612419 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -2.672612419 + 1.428571429 x = -2.672612419 + 1.428571429 Combine like terms: -2.672612419 + 1.428571429 = -1.24404099 x = -1.24404099 Simplifying x = -1.24404099Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.101183848, -1.24404099}
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