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Simplifying 15x + -4.9x2 = 4 Solving 15x + -4.9x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 15x + -4.9x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 15x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.8163265306 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '-0.8163265306' to each side of the equation. 0.8163265306 + -3.06122449x + -0.8163265306 + x2 = 0 + -0.8163265306 Reorder the terms: 0.8163265306 + -0.8163265306 + -3.06122449x + x2 = 0 + -0.8163265306 Combine like terms: 0.8163265306 + -0.8163265306 = 0.0000000000 0.0000000000 + -3.06122449x + x2 = 0 + -0.8163265306 -3.06122449x + x2 = 0 + -0.8163265306 Combine like terms: 0 + -0.8163265306 = -0.8163265306 -3.06122449x + x2 = -0.8163265306 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 = -0.8163265306 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = -0.8163265306 + 2.342773845 Combine like terms: -0.8163265306 + 2.342773845 = 1.5264473144 2.342773845 + -3.06122449x + x2 = 1.5264473144 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 1.5264473144 Calculate the square root of the right side: 1.235494765 Break this problem into two subproblems by setting (x + -1.530612245) equal to 1.235494765 and -1.235494765.Subproblem 1
x + -1.530612245 = 1.235494765 Simplifying x + -1.530612245 = 1.235494765 Reorder the terms: -1.530612245 + x = 1.235494765 Solving -1.530612245 + x = 1.235494765 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 = 1.235494765 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 1.235494765 + 1.530612245 x = 1.235494765 + 1.530612245 Combine like terms: 1.235494765 + 1.530612245 = 2.76610701 x = 2.76610701 Simplifying x = 2.76610701Subproblem 2
x + -1.530612245 = -1.235494765 Simplifying x + -1.530612245 = -1.235494765 Reorder the terms: -1.530612245 + x = -1.235494765 Solving -1.530612245 + x = -1.235494765 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 = -1.235494765 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -1.235494765 + 1.530612245 x = -1.235494765 + 1.530612245 Combine like terms: -1.235494765 + 1.530612245 = 0.29511748 x = 0.29511748 Simplifying x = 0.29511748Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.76610701, 0.29511748}
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