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Simplifying 0 = 4.9x2 + -15x + 7 Reorder the terms: 0 = 7 + -15x + 4.9x2 Solving 0 = 7 + -15x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + 15x + -4.9x2 = 7 + -15x + 4.9x2 + -7 + 15x + -4.9x2 Reorder the terms: -7 + 15x + -4.9x2 = 7 + -7 + -15x + 15x + 4.9x2 + -4.9x2 Combine like terms: 7 + -7 = 0 -7 + 15x + -4.9x2 = 0 + -15x + 15x + 4.9x2 + -4.9x2 -7 + 15x + -4.9x2 = -15x + 15x + 4.9x2 + -4.9x2 Combine like terms: -15x + 15x = 0 -7 + 15x + -4.9x2 = 0 + 4.9x2 + -4.9x2 -7 + 15x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 -7 + 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'. 1.428571429 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + -3.06122449x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + -3.06122449x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + -3.06122449x + x2 = 0 + -1.428571429 -3.06122449x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 -3.06122449x + x2 = -1.428571429 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 = -1.428571429 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = -1.428571429 + 2.342773845 Combine like terms: -1.428571429 + 2.342773845 = 0.914202416 2.342773845 + -3.06122449x + x2 = 0.914202416 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 0.914202416 Calculate the square root of the right side: 0.956139329 Break this problem into two subproblems by setting (x + -1.530612245) equal to 0.956139329 and -0.956139329.Subproblem 1
x + -1.530612245 = 0.956139329 Simplifying x + -1.530612245 = 0.956139329 Reorder the terms: -1.530612245 + x = 0.956139329 Solving -1.530612245 + x = 0.956139329 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 = 0.956139329 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 0.956139329 + 1.530612245 x = 0.956139329 + 1.530612245 Combine like terms: 0.956139329 + 1.530612245 = 2.486751574 x = 2.486751574 Simplifying x = 2.486751574Subproblem 2
x + -1.530612245 = -0.956139329 Simplifying x + -1.530612245 = -0.956139329 Reorder the terms: -1.530612245 + x = -0.956139329 Solving -1.530612245 + x = -0.956139329 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 = -0.956139329 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -0.956139329 + 1.530612245 x = -0.956139329 + 1.530612245 Combine like terms: -0.956139329 + 1.530612245 = 0.574472916 x = 0.574472916 Simplifying x = 0.574472916Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.486751574, 0.574472916}
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