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Simplifying 3x2 = (4x + -4 + 9) * 0.9 Reorder the terms: 3x2 = (-4 + 9 + 4x) * 0.9 Combine like terms: -4 + 9 = 5 3x2 = (5 + 4x) * 0.9 Reorder the terms for easier multiplication: 3x2 = 0.9(5 + 4x) 3x2 = (5 * 0.9 + 4x * 0.9) 3x2 = (4.5 + 3.6x) Solving 3x2 = 4.5 + 3.6x Solving for variable 'x'. Reorder the terms: -4.5 + -3.6x + 3x2 = 4.5 + 3.6x + -4.5 + -3.6x Reorder the terms: -4.5 + -3.6x + 3x2 = 4.5 + -4.5 + 3.6x + -3.6x Combine like terms: 4.5 + -4.5 = 0.0 -4.5 + -3.6x + 3x2 = 0.0 + 3.6x + -3.6x -4.5 + -3.6x + 3x2 = 3.6x + -3.6x Combine like terms: 3.6x + -3.6x = 0.0 -4.5 + -3.6x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.5 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.2x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.2x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.2x + x2 = 0.0 + 1.5 -1.2x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -1.2x + x2 = 1.5 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 1.5 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.5 + 0.36 Combine like terms: 1.5 + 0.36 = 1.86 0.36 + -1.2x + x2 = 1.86 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.86 Calculate the square root of the right side: 1.36381817 Break this problem into two subproblems by setting (x + -0.6) equal to 1.36381817 and -1.36381817.Subproblem 1
x + -0.6 = 1.36381817 Simplifying x + -0.6 = 1.36381817 Reorder the terms: -0.6 + x = 1.36381817 Solving -0.6 + x = 1.36381817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.36381817 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.36381817 + 0.6 x = 1.36381817 + 0.6 Combine like terms: 1.36381817 + 0.6 = 1.96381817 x = 1.96381817 Simplifying x = 1.96381817Subproblem 2
x + -0.6 = -1.36381817 Simplifying x + -0.6 = -1.36381817 Reorder the terms: -0.6 + x = -1.36381817 Solving -0.6 + x = -1.36381817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.36381817 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.36381817 + 0.6 x = -1.36381817 + 0.6 Combine like terms: -1.36381817 + 0.6 = -0.76381817 x = -0.76381817 Simplifying x = -0.76381817Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.96381817, -0.76381817}
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