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Simplifying 3x + 22 = 10x2 Reorder the terms: 22 + 3x = 10x2 Solving 22 + 3x = 10x2 Solving for variable 'x'. Combine like terms: 10x2 + -10x2 = 0 22 + 3x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -2.2 + -0.3x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -0.3x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -0.3x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -0.3x + x2 = 0 + 2.2 -0.3x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -0.3x + x2 = 2.2 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 2.2 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 2.2 + 0.0225 Combine like terms: 2.2 + 0.0225 = 2.2225 0.0225 + -0.3x + x2 = 2.2225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 2.2225 Calculate the square root of the right side: 1.490805152 Break this problem into two subproblems by setting (x + -0.15) equal to 1.490805152 and -1.490805152.Subproblem 1
x + -0.15 = 1.490805152 Simplifying x + -0.15 = 1.490805152 Reorder the terms: -0.15 + x = 1.490805152 Solving -0.15 + x = 1.490805152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 1.490805152 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.490805152 + 0.15 x = 1.490805152 + 0.15 Combine like terms: 1.490805152 + 0.15 = 1.640805152 x = 1.640805152 Simplifying x = 1.640805152Subproblem 2
x + -0.15 = -1.490805152 Simplifying x + -0.15 = -1.490805152 Reorder the terms: -0.15 + x = -1.490805152 Solving -0.15 + x = -1.490805152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -1.490805152 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.490805152 + 0.15 x = -1.490805152 + 0.15 Combine like terms: -1.490805152 + 0.15 = -1.340805152 x = -1.340805152 Simplifying x = -1.340805152Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.640805152, -1.340805152}
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