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Simplifying 10x2 + 6x + -23 = 0 Reorder the terms: -23 + 6x + 10x2 = 0 Solving -23 + 6x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.3 + 0.6x + x2 = 0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + 0.6x + 2.3 + x2 = 0 + 2.3 Reorder the terms: -2.3 + 2.3 + 0.6x + x2 = 0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + 0.6x + x2 = 0 + 2.3 0.6x + x2 = 0 + 2.3 Combine like terms: 0 + 2.3 = 2.3 0.6x + x2 = 2.3 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 = 2.3 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 2.3 + 0.09 Combine like terms: 2.3 + 0.09 = 2.39 0.09 + 0.6x + x2 = 2.39 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 2.39 Calculate the square root of the right side: 1.545962483 Break this problem into two subproblems by setting (x + 0.3) equal to 1.545962483 and -1.545962483.Subproblem 1
x + 0.3 = 1.545962483 Simplifying x + 0.3 = 1.545962483 Reorder the terms: 0.3 + x = 1.545962483 Solving 0.3 + x = 1.545962483 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 = 1.545962483 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.545962483 + -0.3 x = 1.545962483 + -0.3 Combine like terms: 1.545962483 + -0.3 = 1.245962483 x = 1.245962483 Simplifying x = 1.245962483Subproblem 2
x + 0.3 = -1.545962483 Simplifying x + 0.3 = -1.545962483 Reorder the terms: 0.3 + x = -1.545962483 Solving 0.3 + x = -1.545962483 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 = -1.545962483 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.545962483 + -0.3 x = -1.545962483 + -0.3 Combine like terms: -1.545962483 + -0.3 = -1.845962483 x = -1.845962483 Simplifying x = -1.845962483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.245962483, -1.845962483}
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