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Simplifying 0.91x2 + -0.54x + -4.9 = 0 Reorder the terms: -4.9 + -0.54x + 0.91x2 = 0 Solving -4.9 + -0.54x + 0.91x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.91 the coefficient of the squared term: Divide each side by '0.91'. -5.384615385 + -0.5934065934x + x2 = 0 Move the constant term to the right: Add '5.384615385' to each side of the equation. -5.384615385 + -0.5934065934x + 5.384615385 + x2 = 0 + 5.384615385 Reorder the terms: -5.384615385 + 5.384615385 + -0.5934065934x + x2 = 0 + 5.384615385 Combine like terms: -5.384615385 + 5.384615385 = 0.000000000 0.000000000 + -0.5934065934x + x2 = 0 + 5.384615385 -0.5934065934x + x2 = 0 + 5.384615385 Combine like terms: 0 + 5.384615385 = 5.384615385 -0.5934065934x + x2 = 5.384615385 The x term is -0.5934065934x. Take half its coefficient (-0.2967032967). Square it (0.08803284627) and add it to both sides. Add '0.08803284627' to each side of the equation. -0.5934065934x + 0.08803284627 + x2 = 5.384615385 + 0.08803284627 Reorder the terms: 0.08803284627 + -0.5934065934x + x2 = 5.384615385 + 0.08803284627 Combine like terms: 5.384615385 + 0.08803284627 = 5.47264823127 0.08803284627 + -0.5934065934x + x2 = 5.47264823127 Factor a perfect square on the left side: (x + -0.2967032967)(x + -0.2967032967) = 5.47264823127 Calculate the square root of the right side: 2.339369195 Break this problem into two subproblems by setting (x + -0.2967032967) equal to 2.339369195 and -2.339369195.Subproblem 1
x + -0.2967032967 = 2.339369195 Simplifying x + -0.2967032967 = 2.339369195 Reorder the terms: -0.2967032967 + x = 2.339369195 Solving -0.2967032967 + x = 2.339369195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2967032967' to each side of the equation. -0.2967032967 + 0.2967032967 + x = 2.339369195 + 0.2967032967 Combine like terms: -0.2967032967 + 0.2967032967 = 0.0000000000 0.0000000000 + x = 2.339369195 + 0.2967032967 x = 2.339369195 + 0.2967032967 Combine like terms: 2.339369195 + 0.2967032967 = 2.6360724917 x = 2.6360724917 Simplifying x = 2.6360724917Subproblem 2
x + -0.2967032967 = -2.339369195 Simplifying x + -0.2967032967 = -2.339369195 Reorder the terms: -0.2967032967 + x = -2.339369195 Solving -0.2967032967 + x = -2.339369195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2967032967' to each side of the equation. -0.2967032967 + 0.2967032967 + x = -2.339369195 + 0.2967032967 Combine like terms: -0.2967032967 + 0.2967032967 = 0.0000000000 0.0000000000 + x = -2.339369195 + 0.2967032967 x = -2.339369195 + 0.2967032967 Combine like terms: -2.339369195 + 0.2967032967 = -2.0426658983 x = -2.0426658983 Simplifying x = -2.0426658983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6360724917, -2.0426658983}
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