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Simplifying 38x2 + -4.8x + -0.288 = 0 Reorder the terms: -0.288 + -4.8x + 38x2 = 0 Solving -0.288 + -4.8x + 38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. -0.007578947368 + -0.1263157895x + x2 = 0 Move the constant term to the right: Add '0.007578947368' to each side of the equation. -0.007578947368 + -0.1263157895x + 0.007578947368 + x2 = 0 + 0.007578947368 Reorder the terms: -0.007578947368 + 0.007578947368 + -0.1263157895x + x2 = 0 + 0.007578947368 Combine like terms: -0.007578947368 + 0.007578947368 = 0.000000000000 0.000000000000 + -0.1263157895x + x2 = 0 + 0.007578947368 -0.1263157895x + x2 = 0 + 0.007578947368 Combine like terms: 0 + 0.007578947368 = 0.007578947368 -0.1263157895x + x2 = 0.007578947368 The x term is -0.1263157895x. Take half its coefficient (-0.06315789475). Square it (0.003988919669) and add it to both sides. Add '0.003988919669' to each side of the equation. -0.1263157895x + 0.003988919669 + x2 = 0.007578947368 + 0.003988919669 Reorder the terms: 0.003988919669 + -0.1263157895x + x2 = 0.007578947368 + 0.003988919669 Combine like terms: 0.007578947368 + 0.003988919669 = 0.011567867037 0.003988919669 + -0.1263157895x + x2 = 0.011567867037 Factor a perfect square on the left side: (x + -0.06315789475)(x + -0.06315789475) = 0.011567867037 Calculate the square root of the right side: 0.107554019 Break this problem into two subproblems by setting (x + -0.06315789475) equal to 0.107554019 and -0.107554019.Subproblem 1
x + -0.06315789475 = 0.107554019 Simplifying x + -0.06315789475 = 0.107554019 Reorder the terms: -0.06315789475 + x = 0.107554019 Solving -0.06315789475 + x = 0.107554019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06315789475' to each side of the equation. -0.06315789475 + 0.06315789475 + x = 0.107554019 + 0.06315789475 Combine like terms: -0.06315789475 + 0.06315789475 = 0.00000000000 0.00000000000 + x = 0.107554019 + 0.06315789475 x = 0.107554019 + 0.06315789475 Combine like terms: 0.107554019 + 0.06315789475 = 0.17071191375 x = 0.17071191375 Simplifying x = 0.17071191375Subproblem 2
x + -0.06315789475 = -0.107554019 Simplifying x + -0.06315789475 = -0.107554019 Reorder the terms: -0.06315789475 + x = -0.107554019 Solving -0.06315789475 + x = -0.107554019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06315789475' to each side of the equation. -0.06315789475 + 0.06315789475 + x = -0.107554019 + 0.06315789475 Combine like terms: -0.06315789475 + 0.06315789475 = 0.00000000000 0.00000000000 + x = -0.107554019 + 0.06315789475 x = -0.107554019 + 0.06315789475 Combine like terms: -0.107554019 + 0.06315789475 = -0.04439612425 x = -0.04439612425 Simplifying x = -0.04439612425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17071191375, -0.04439612425}
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