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Simplifying 4.3x2 + -5.3x + 1.5 = 16.7x + 3 Reorder the terms: 1.5 + -5.3x + 4.3x2 = 16.7x + 3 Reorder the terms: 1.5 + -5.3x + 4.3x2 = 3 + 16.7x Solving 1.5 + -5.3x + 4.3x2 = 3 + 16.7x Solving for variable 'x'. Reorder the terms: 1.5 + -3 + -5.3x + -16.7x + 4.3x2 = 3 + 16.7x + -3 + -16.7x Combine like terms: 1.5 + -3 = -1.5 -1.5 + -5.3x + -16.7x + 4.3x2 = 3 + 16.7x + -3 + -16.7x Combine like terms: -5.3x + -16.7x = -22x -1.5 + -22x + 4.3x2 = 3 + 16.7x + -3 + -16.7x Reorder the terms: -1.5 + -22x + 4.3x2 = 3 + -3 + 16.7x + -16.7x Combine like terms: 3 + -3 = 0 -1.5 + -22x + 4.3x2 = 0 + 16.7x + -16.7x -1.5 + -22x + 4.3x2 = 16.7x + -16.7x Combine like terms: 16.7x + -16.7x = 0.0 -1.5 + -22x + 4.3x2 = 0.0 Begin completing the square. Divide all terms by 4.3 the coefficient of the squared term: Divide each side by '4.3'. -0.3488372093 + -5.11627907x + x2 = 0 Move the constant term to the right: Add '0.3488372093' to each side of the equation. -0.3488372093 + -5.11627907x + 0.3488372093 + x2 = 0 + 0.3488372093 Reorder the terms: -0.3488372093 + 0.3488372093 + -5.11627907x + x2 = 0 + 0.3488372093 Combine like terms: -0.3488372093 + 0.3488372093 = 0.0000000000 0.0000000000 + -5.11627907x + x2 = 0 + 0.3488372093 -5.11627907x + x2 = 0 + 0.3488372093 Combine like terms: 0 + 0.3488372093 = 0.3488372093 -5.11627907x + x2 = 0.3488372093 The x term is -5.11627907x. Take half its coefficient (-2.558139535). Square it (6.544077881) and add it to both sides. Add '6.544077881' to each side of the equation. -5.11627907x + 6.544077881 + x2 = 0.3488372093 + 6.544077881 Reorder the terms: 6.544077881 + -5.11627907x + x2 = 0.3488372093 + 6.544077881 Combine like terms: 0.3488372093 + 6.544077881 = 6.8929150903 6.544077881 + -5.11627907x + x2 = 6.8929150903 Factor a perfect square on the left side: (x + -2.558139535)(x + -2.558139535) = 6.8929150903 Calculate the square root of the right side: 2.625436171 Break this problem into two subproblems by setting (x + -2.558139535) equal to 2.625436171 and -2.625436171.Subproblem 1
x + -2.558139535 = 2.625436171 Simplifying x + -2.558139535 = 2.625436171 Reorder the terms: -2.558139535 + x = 2.625436171 Solving -2.558139535 + x = 2.625436171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.558139535' to each side of the equation. -2.558139535 + 2.558139535 + x = 2.625436171 + 2.558139535 Combine like terms: -2.558139535 + 2.558139535 = 0.000000000 0.000000000 + x = 2.625436171 + 2.558139535 x = 2.625436171 + 2.558139535 Combine like terms: 2.625436171 + 2.558139535 = 5.183575706 x = 5.183575706 Simplifying x = 5.183575706Subproblem 2
x + -2.558139535 = -2.625436171 Simplifying x + -2.558139535 = -2.625436171 Reorder the terms: -2.558139535 + x = -2.625436171 Solving -2.558139535 + x = -2.625436171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.558139535' to each side of the equation. -2.558139535 + 2.558139535 + x = -2.625436171 + 2.558139535 Combine like terms: -2.558139535 + 2.558139535 = 0.000000000 0.000000000 + x = -2.625436171 + 2.558139535 x = -2.625436171 + 2.558139535 Combine like terms: -2.625436171 + 2.558139535 = -0.067296636 x = -0.067296636 Simplifying x = -0.067296636Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.183575706, -0.067296636}
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