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Simplifying 10x2 + -19 = -6x Reorder the terms: -19 + 10x2 = -6x Solving -19 + 10x2 = -6x Solving for variable 'x'. Reorder the terms: -19 + 6x + 10x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -19 + 6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 0.6x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + 0.6x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 0.6x + x2 = 0 + 1.9 0.6x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 0.6x + x2 = 1.9 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.9 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.9 + 0.09 Combine like terms: 1.9 + 0.09 = 1.99 0.09 + 0.6x + x2 = 1.99 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.99 Calculate the square root of the right side: 1.410673598 Break this problem into two subproblems by setting (x + 0.3) equal to 1.410673598 and -1.410673598.Subproblem 1
x + 0.3 = 1.410673598 Simplifying x + 0.3 = 1.410673598 Reorder the terms: 0.3 + x = 1.410673598 Solving 0.3 + x = 1.410673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.410673598 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.410673598 + -0.3 x = 1.410673598 + -0.3 Combine like terms: 1.410673598 + -0.3 = 1.110673598 x = 1.110673598 Simplifying x = 1.110673598Subproblem 2
x + 0.3 = -1.410673598 Simplifying x + 0.3 = -1.410673598 Reorder the terms: 0.3 + x = -1.410673598 Solving 0.3 + x = -1.410673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.410673598 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.410673598 + -0.3 x = -1.410673598 + -0.3 Combine like terms: -1.410673598 + -0.3 = -1.710673598 x = -1.710673598 Simplifying x = -1.710673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.110673598, -1.710673598}
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