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Simplifying 1.8x2 + -7.5x + -0.4 = 4.6 Reorder the terms: -0.4 + -7.5x + 1.8x2 = 4.6 Solving -0.4 + -7.5x + 1.8x2 = 4.6 Solving for variable 'x'. Reorder the terms: -0.4 + -4.6 + -7.5x + 1.8x2 = 4.6 + -4.6 Combine like terms: -0.4 + -4.6 = -5 -5 + -7.5x + 1.8x2 = 4.6 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 -5 + -7.5x + 1.8x2 = 0.0 Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. -2.777777778 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -4.166666667x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -4.166666667x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -4.166666667x + x2 = 0 + 2.777777778 -4.166666667x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -4.166666667x + x2 = 2.777777778 The x term is -4.166666667x. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667x + 4.340277781 + x2 = 2.777777778 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = 2.777777778 + 4.340277781 Combine like terms: 2.777777778 + 4.340277781 = 7.118055559 4.340277781 + -4.166666667x + x2 = 7.118055559 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 7.118055559 Calculate the square root of the right side: 2.667968433 Break this problem into two subproblems by setting (x + -2.083333334) equal to 2.667968433 and -2.667968433.Subproblem 1
x + -2.083333334 = 2.667968433 Simplifying x + -2.083333334 = 2.667968433 Reorder the terms: -2.083333334 + x = 2.667968433 Solving -2.083333334 + x = 2.667968433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = 2.667968433 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 2.667968433 + 2.083333334 x = 2.667968433 + 2.083333334 Combine like terms: 2.667968433 + 2.083333334 = 4.751301767 x = 4.751301767 Simplifying x = 4.751301767Subproblem 2
x + -2.083333334 = -2.667968433 Simplifying x + -2.083333334 = -2.667968433 Reorder the terms: -2.083333334 + x = -2.667968433 Solving -2.083333334 + x = -2.667968433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = -2.667968433 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -2.667968433 + 2.083333334 x = -2.667968433 + 2.083333334 Combine like terms: -2.667968433 + 2.083333334 = -0.584635099 x = -0.584635099 Simplifying x = -0.584635099Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.751301767, -0.584635099}
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