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Simplifying 15(x) = 28 + -4.9x2 Solving 15x = 28 + -4.9x2 Solving for variable 'x'. Reorder the terms: -28 + 15x + 4.9x2 = 28 + -4.9x2 + -28 + 4.9x2 Reorder the terms: -28 + 15x + 4.9x2 = 28 + -28 + -4.9x2 + 4.9x2 Combine like terms: 28 + -28 = 0 -28 + 15x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -28 + 15x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -28 + 15x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -5.714285714 + 3.06122449x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 3.06122449x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 3.06122449x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 3.06122449x + x2 = 0 + 5.714285714 3.06122449x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 3.06122449x + x2 = 5.714285714 The x term is 3.06122449x. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449x + 2.342773845 + x2 = 5.714285714 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449x + x2 = 5.714285714 + 2.342773845 Combine like terms: 5.714285714 + 2.342773845 = 8.057059559 2.342773845 + 3.06122449x + x2 = 8.057059559 Factor a perfect square on the left side: (x + 1.530612245)(x + 1.530612245) = 8.057059559 Calculate the square root of the right side: 2.838496003 Break this problem into two subproblems by setting (x + 1.530612245) equal to 2.838496003 and -2.838496003.Subproblem 1
x + 1.530612245 = 2.838496003 Simplifying x + 1.530612245 = 2.838496003 Reorder the terms: 1.530612245 + x = 2.838496003 Solving 1.530612245 + x = 2.838496003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + x = 2.838496003 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = 2.838496003 + -1.530612245 x = 2.838496003 + -1.530612245 Combine like terms: 2.838496003 + -1.530612245 = 1.307883758 x = 1.307883758 Simplifying x = 1.307883758Subproblem 2
x + 1.530612245 = -2.838496003 Simplifying x + 1.530612245 = -2.838496003 Reorder the terms: 1.530612245 + x = -2.838496003 Solving 1.530612245 + x = -2.838496003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + x = -2.838496003 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = -2.838496003 + -1.530612245 x = -2.838496003 + -1.530612245 Combine like terms: -2.838496003 + -1.530612245 = -4.369108248 x = -4.369108248 Simplifying x = -4.369108248Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.307883758, -4.369108248}
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