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Simplifying 4.9x2 + -15x + -18.6 = 0 Reorder the terms: -18.6 + -15x + 4.9x2 = 0 Solving -18.6 + -15x + 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'. -3.795918367 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '3.795918367' to each side of the equation. -3.795918367 + -3.06122449x + 3.795918367 + x2 = 0 + 3.795918367 Reorder the terms: -3.795918367 + 3.795918367 + -3.06122449x + x2 = 0 + 3.795918367 Combine like terms: -3.795918367 + 3.795918367 = 0.000000000 0.000000000 + -3.06122449x + x2 = 0 + 3.795918367 -3.06122449x + x2 = 0 + 3.795918367 Combine like terms: 0 + 3.795918367 = 3.795918367 -3.06122449x + x2 = 3.795918367 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 = 3.795918367 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 3.795918367 + 2.342773845 Combine like terms: 3.795918367 + 2.342773845 = 6.138692212 2.342773845 + -3.06122449x + x2 = 6.138692212 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 6.138692212 Calculate the square root of the right side: 2.477638434 Break this problem into two subproblems by setting (x + -1.530612245) equal to 2.477638434 and -2.477638434.Subproblem 1
x + -1.530612245 = 2.477638434 Simplifying x + -1.530612245 = 2.477638434 Reorder the terms: -1.530612245 + x = 2.477638434 Solving -1.530612245 + x = 2.477638434 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 = 2.477638434 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 2.477638434 + 1.530612245 x = 2.477638434 + 1.530612245 Combine like terms: 2.477638434 + 1.530612245 = 4.008250679 x = 4.008250679 Simplifying x = 4.008250679Subproblem 2
x + -1.530612245 = -2.477638434 Simplifying x + -1.530612245 = -2.477638434 Reorder the terms: -1.530612245 + x = -2.477638434 Solving -1.530612245 + x = -2.477638434 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 = -2.477638434 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -2.477638434 + 1.530612245 x = -2.477638434 + 1.530612245 Combine like terms: -2.477638434 + 1.530612245 = -0.947026189 x = -0.947026189 Simplifying x = -0.947026189Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.008250679, -0.947026189}
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